118:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000
Propiedades de los logaritmos:@0.404236:0.098585:0.645203:0.098585:0.645203:0.080902:0.404236:0.080902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema. :@0.404236:0.115654:0.476038:0.115654:0.476038:0.098882:0.404236:0.098882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   > 0,   ≠ 1 base de la función logarítmica :@0.475922:0.115293:0.804470:0.115293:0.804470:0.098795:0.475922:0.098795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.504088:0.115408:0.513066:0.115408:0.513066:0.098940:0.504088:0.098940:0.000000
a:@0.547261:0.115408:0.556239:0.115408:0.556239:0.098940:0.547261:0.098940:0.000000
Log:@0.804374:0.115408:0.828164:0.115408:0.828164:0.098940:0.804374:0.098940:0.000000:0.000000:0.000000
a:@0.828308:0.118638:0.833542:0.118638:0.833542:0.109037:0.828308:0.109037:0.000000
. Se veri-:@0.833541:0.115293:0.891779:0.115293:0.891779:0.098795:0.833541:0.098795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fican las siguientes propiedades.:@0.404235:0.132643:0.629944:0.132643:0.629944:0.116146:0.404235:0.116146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
i):@0.404235:0.167562:0.414773:0.167562:0.414773:0.150847:0.404235:0.150847:0.000000:0.000000
 :@0.414773:0.167345:0.418915:0.167345:0.418915:0.150847:0.414773:0.150847:0.000000
log:@0.427969:0.167461:0.447832:0.167461:0.447832:0.150992:0.427969:0.150992:0.000000:0.000000:0.000000
a:@0.448034:0.170690:0.453268:0.170690:0.453268:0.161089:0.448034:0.161089:0.000000
( ) = :@0.453269:0.167345:0.503186:0.167345:0.503186:0.150847:0.453269:0.150847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
αβ:@0.459221:0.173906:0.478134:0.173906:0.478134:0.156635:0.459221:0.156635:0.000000:0.000000
log:@0.503186:0.167461:0.523048:0.167461:0.523048:0.150992:0.503186:0.150992:0.000000:0.000000:0.000000
a:@0.523240:0.170690:0.528474:0.170690:0.528474:0.161089:0.523240:0.161089:0.000000
( ) + :@0.528474:0.167345:0.569090:0.167345:0.569090:0.150847:0.528474:0.150847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.534426:0.173906:0.544042:0.173906:0.544042:0.156635:0.534426:0.156635:0.000000
log:@0.569090:0.167461:0.588952:0.167461:0.588952:0.150992:0.569090:0.150992:0.000000:0.000000:0.000000
a:@0.589144:0.170690:0.594378:0.170690:0.594378:0.161089:0.589144:0.161089:0.000000
( ),    :@0.594379:0.167345:0.634908:0.167345:0.634908:0.150847:0.594379:0.150847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
β:@0.600331:0.173906:0.609629:0.173906:0.609629:0.156635:0.600331:0.156635:0.000000
∀:@0.634907:0.174931:0.646479:0.174931:0.646479:0.155932:0.634907:0.155932:0.000000
α β:@0.646488:0.173906:0.672301:0.173906:0.672301:0.156635:0.646488:0.156635:0.000000:0.000000:0.000000
,     :@0.656107:0.167345:0.695241:0.167345:0.695241:0.150847:0.656107:0.150847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.676446:0.166826:0.691098:0.166826:0.691098:0.153453:0.676446:0.153453:0.000000
:@0.695240:0.166258:0.708545:0.166258:0.708545:0.153396:0.695240:0.153396:0.000000
+:@0.708545:0.159736:0.714846:0.159736:0.714846:0.150118:0.708545:0.150118:0.000000
.:@0.714846:0.167345:0.717601:0.167345:0.717601:0.150847:0.714846:0.150847:0.000000
ii):@0.404232:0.195598:0.419028:0.195598:0.419028:0.178883:0.404232:0.178883:0.000000:0.000000:0.000000
 :@0.419028:0.195381:0.423170:0.195381:0.423170:0.178883:0.419028:0.178883:0.000000
log:@0.427967:0.195496:0.447829:0.195496:0.447829:0.179028:0.427967:0.179028:0.000000:0.000000:0.000000
a:@0.448034:0.198733:0.453268:0.198733:0.453268:0.189132:0.448034:0.189132:0.000000
        = :@0.453269:0.195388:0.501355:0.195388:0.501355:0.178890:0.453269:0.178890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.501355:0.195503:0.521215:0.195503:0.521215:0.179035:0.501355:0.179035:0.000000:0.000000:0.000000
a:@0.521407:0.198733:0.526641:0.198733:0.526641:0.189132:0.521407:0.189132:0.000000
( ) – :@0.526641:0.195388:0.566951:0.195388:0.566951:0.178890:0.526641:0.178890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.532595:0.201949:0.542211:0.201949:0.542211:0.184677:0.532595:0.184677:0.000000
log:@0.566951:0.195503:0.586813:0.195503:0.586813:0.179035:0.566951:0.179035:0.000000:0.000000:0.000000
a:@0.587005:0.198733:0.592239:0.198733:0.592239:0.189132:0.587005:0.189132:0.000000
( ),    :@0.592238:0.195388:0.634501:0.195388:0.634501:0.178890:0.592238:0.178890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
β:@0.598190:0.201949:0.607488:0.201949:0.607488:0.184677:0.598190:0.184677:0.000000
∀:@0.635079:0.202974:0.646652:0.202974:0.646652:0.183975:0.635079:0.183975:0.000000
α β:@0.646658:0.201949:0.672472:0.201949:0.672472:0.184677:0.646658:0.184677:0.000000:0.000000:0.000000
,     :@0.656279:0.195388:0.695412:0.195388:0.695412:0.178890:0.656279:0.178890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.676618:0.194869:0.691271:0.194869:0.691271:0.181496:0.676618:0.181496:0.000000
:@0.695413:0.194301:0.708718:0.194301:0.708718:0.181439:0.695413:0.181439:0.000000
+:@0.708716:0.187779:0.715017:0.187779:0.715017:0.178161:0.708716:0.178161:0.000000
.:@0.715018:0.195388:0.717773:0.195388:0.717773:0.178890:0.715018:0.178890:0.000000
iii):@0.404231:0.227212:0.423284:0.227212:0.423284:0.210497:0.404231:0.210497:0.000000:0.000000:0.000000:0.000000
 :@0.423284:0.226995:0.427427:0.226995:0.427427:0.210497:0.423284:0.210497:0.000000
log:@0.427966:0.227111:0.447828:0.227111:0.447828:0.210642:0.427966:0.210642:0.000000:0.000000:0.000000
a:@0.448034:0.230339:0.453268:0.230339:0.453268:0.220738:0.448034:0.220738:0.000000
(    ) =      :@0.453269:0.226995:0.527021:0.226995:0.527021:0.210497:0.453269:0.210497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.459221:0.233557:0.468837:0.233557:0.468837:0.216285:0.459221:0.216285:0.000000
log:@0.527021:0.227111:0.546884:0.227111:0.546884:0.210642:0.527021:0.210642:0.000000:0.000000:0.000000
a:@0.547075:0.230339:0.552309:0.230339:0.552309:0.220738:0.547075:0.220738:0.000000
( ),               :@0.552309:0.226995:0.636022:0.226995:0.636022:0.210497:0.552309:0.210497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.558261:0.233557:0.567877:0.233557:0.567877:0.216285:0.558261:0.216285:0.000000
∀:@0.635828:0.234581:0.647401:0.234581:0.647401:0.215582:0.635828:0.215582:0.000000
α:@0.647409:0.233557:0.657025:0.233557:0.657025:0.216285:0.647409:0.216285:0.000000
   :@0.657028:0.226995:0.679965:0.226995:0.679965:0.210497:0.657028:0.210497:0.000000:0.000000:0.000000
:@0.661169:0.226476:0.675822:0.226476:0.675822:0.213103:0.661169:0.213103:0.000000
:@0.679964:0.225908:0.693269:0.225908:0.693269:0.213046:0.679964:0.213046:0.000000
+:@0.693269:0.219385:0.699570:0.219385:0.699570:0.209767:0.693269:0.209767:0.000000
, :@0.699569:0.226995:0.706466:0.226995:0.706466:0.210497:0.699569:0.210497:0.000000:0.000000
∀:@0.706466:0.234581:0.718039:0.234581:0.718039:0.215582:0.706466:0.215582:0.000000
m, n:@0.718047:0.227111:0.748891:0.227111:0.748891:0.210642:0.718047:0.210642:0.000000:0.000000:0.000000:0.000000
     con   ≠ 0.:@0.748891:0.226995:0.859059:0.226995:0.859059:0.210497:0.748891:0.210497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.753031:0.226476:0.767684:0.226476:0.767684:0.213103:0.753031:0.213103:0.000000
Z:@0.771826:0.225908:0.784117:0.225908:0.784117:0.213046:0.771826:0.213046:0.000000
n:@0.819353:0.227111:0.828716:0.227111:0.828716:0.210642:0.819353:0.210642:0.000000
Demostración  :@0.404245:0.262159:0.520915:0.262159:0.520915:0.245213:0.404245:0.245213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.513536:0.261913:0.516889:0.261913:0.516889:0.245199:0.513536:0.245199:0.000000
Sean  ,     :@0.520915:0.261697:0.607455:0.261697:0.607455:0.245199:0.520915:0.245199:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α β:@0.558702:0.268258:0.584515:0.268258:0.584515:0.250986:0.558702:0.250986:0.000000:0.000000:0.000000
:@0.588662:0.261178:0.603314:0.261178:0.603314:0.247805:0.588662:0.247805:0.000000
:@0.607454:0.260610:0.620759:0.260610:0.620759:0.247747:0.607454:0.247747:0.000000
+:@0.620759:0.254086:0.627060:0.254086:0.627060:0.244468:0.620759:0.244468:0.000000
.:@0.627060:0.261697:0.629815:0.261697:0.629815:0.245199:0.627060:0.245199:0.000000
i):@0.404238:0.279264:0.414776:0.279264:0.414776:0.262550:0.404238:0.262550:0.000000:0.000000
  De la definición de las funciones :@0.414776:0.279047:0.657824:0.279047:0.657824:0.262550:0.414776:0.262550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Exp:@0.657054:0.279163:0.682195:0.279163:0.682195:0.262694:0.657054:0.262694:0.000000:0.000000:0.000000
a:@0.682286:0.282393:0.687520:0.282393:0.687520:0.272791:0.682286:0.272791:0.000000
 y :@0.687519:0.279047:0.702854:0.279047:0.702854:0.262550:0.687519:0.262550:0.000000:0.000000:0.000000
Log:@0.702084:0.279163:0.725876:0.279163:0.725876:0.262694:0.702084:0.262694:0.000000:0.000000:0.000000
a:@0.726072:0.282393:0.731305:0.282393:0.731305:0.272791:0.726072:0.272791:0.000000
 se tienen las siguientes :@0.731307:0.279047:0.895907:0.279047:0.895907:0.262550:0.731307:0.262550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
equivalencias::@0.427975:0.296398:0.525091:0.296398:0.525091:0.279900:0.427975:0.279900:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404240:0.313749:0.408382:0.313749:0.408382:0.297251:0.404240:0.297251:0.000000
u log:@0.427975:0.313864:0.476138:0.313864:0.476138:0.297396:0.427975:0.297396:0.000000:0.000000:0.000000:0.000000:0.000000
 = :@0.437184:0.313749:0.456276:0.313749:0.456276:0.297251:0.437184:0.297251:0.000000:0.000000:0.000000
a:@0.476335:0.317093:0.481569:0.317093:0.481569:0.307492:0.476335:0.307492:0.000000
( )     = :@0.481569:0.313749:0.557545:0.313749:0.557545:0.297251:0.481569:0.297251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.487521:0.320310:0.497137:0.320310:0.497137:0.303038:0.487521:0.303038:0.000000
⇔:@0.507235:0.312828:0.524691:0.312828:0.524691:0.297426:0.507235:0.297426:0.000000
α:@0.528834:0.320310:0.538450:0.320310:0.538450:0.303038:0.528834:0.303038:0.000000
exp u:@0.557545:0.313864:0.602116:0.313864:0.602116:0.297396:0.557545:0.297396:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.581721:0.317093:0.586955:0.317093:0.586955:0.307492:0.581721:0.307492:0.000000
( ),:@0.586955:0.313749:0.610824:0.313749:0.610824:0.297251:0.586955:0.297251:0.000000:0.000000:0.000000:0.000000
 :@0.404243:0.331100:0.408385:0.331100:0.408385:0.314602:0.404243:0.314602:0.000000
v log:@0.427978:0.331215:0.474715:0.331215:0.474715:0.314746:0.427978:0.314746:0.000000:0.000000:0.000000:0.000000:0.000000
 = :@0.435761:0.331100:0.454853:0.331100:0.454853:0.314602:0.435761:0.314602:0.000000:0.000000:0.000000
a:@0.474910:0.334444:0.480143:0.334444:0.480143:0.324842:0.474910:0.324842:0.000000
( )     = :@0.480143:0.331100:0.555481:0.331100:0.555481:0.314602:0.480143:0.314602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
β:@0.486095:0.337661:0.495393:0.337661:0.495393:0.320389:0.486095:0.320389:0.000000
⇔:@0.505491:0.330179:0.522947:0.330179:0.522947:0.314777:0.505491:0.314777:0.000000
β:@0.527088:0.337661:0.536386:0.337661:0.536386:0.320389:0.527088:0.320389:0.000000
exp v:@0.555481:0.331215:0.598627:0.331215:0.598627:0.314746:0.555481:0.314746:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.579657:0.334444:0.584891:0.334444:0.584891:0.324842:0.579657:0.324842:0.000000
( ).:@0.584891:0.331100:0.607335:0.331100:0.607335:0.314602:0.584891:0.314602:0.000000:0.000000:0.000000:0.000000
Luego,:@0.427975:0.365801:0.473942:0.365801:0.473942:0.349303:0.427975:0.349303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
αβ:@0.478087:0.372363:0.497001:0.372363:0.497001:0.355091:0.478087:0.355091:0.000000:0.000000
 = :@0.497008:0.365801:0.516099:0.365801:0.516099:0.349303:0.497008:0.349303:0.000000:0.000000:0.000000
exp u exp v:@0.516099:0.365917:0.609772:0.365917:0.609772:0.349448:0.516099:0.349448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.540276:0.369146:0.545510:0.369146:0.545510:0.359545:0.540276:0.359545:0.000000
( ):@0.545511:0.365801:0.566626:0.365801:0.566626:0.349303:0.545511:0.349303:0.000000:0.000000:0.000000
a:@0.590801:0.369146:0.596035:0.369146:0.596035:0.359545:0.590801:0.359545:0.000000
( ) = :@0.596036:0.365801:0.634817:0.365801:0.634817:0.349303:0.596036:0.349303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
exp u  v:@0.634817:0.365917:0.706263:0.365917:0.706263:0.349448:0.634817:0.349448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.658993:0.369146:0.664227:0.369146:0.664227:0.359545:0.658993:0.359545:0.000000
( +  ),:@0.664227:0.365801:0.714971:0.365801:0.714971:0.349303:0.664227:0.349303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404242:0.400503:0.408384:0.400503:0.408384:0.384005:0.404242:0.384005:0.000000
de donde  +   = :@0.427977:0.400503:0.556187:0.400503:0.556187:0.384005:0.427977:0.384005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u  v log:@0.501011:0.400618:0.576050:0.400618:0.576050:0.384149:0.501011:0.384149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.576241:0.403847:0.581475:0.403847:0.581475:0.394245:0.576241:0.394245:0.000000
( ) y consecuentemente,:@0.581475:0.400503:0.767770:0.400503:0.767770:0.384005:0.581475:0.384005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
αβ:@0.587429:0.407064:0.606342:0.407064:0.606342:0.389792:0.587429:0.389792:0.000000:0.000000
log:@0.525242:0.417969:0.545105:0.417969:0.545105:0.401500:0.525242:0.401500:0.000000:0.000000:0.000000
a:@0.545291:0.421197:0.550525:0.421197:0.550525:0.411596:0.545291:0.411596:0.000000
( ) =  +   = :@0.550525:0.417853:0.655618:0.417853:0.655618:0.401356:0.550525:0.401356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
αβ:@0.556477:0.424415:0.575390:0.424415:0.575390:0.407143:0.556477:0.407143:0.000000:0.000000
u  v log:@0.600442:0.417969:0.675480:0.417969:0.675480:0.401500:0.600442:0.401500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.675670:0.421197:0.680904:0.421197:0.680904:0.411596:0.675670:0.411596:0.000000
( ) + :@0.680905:0.417853:0.721522:0.417853:0.721522:0.401356:0.680905:0.401356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.686857:0.424415:0.696473:0.424415:0.696473:0.407143:0.686857:0.407143:0.000000
log:@0.721522:0.417969:0.741384:0.417969:0.741384:0.401500:0.721522:0.401500:0.000000:0.000000:0.000000
a:@0.741576:0.421197:0.746810:0.421197:0.746810:0.411596:0.741576:0.411596:0.000000
( ).:@0.746809:0.417853:0.770770:0.417853:0.770770:0.401356:0.746809:0.401356:0.000000:0.000000:0.000000:0.000000
β:@0.752763:0.424415:0.762061:0.424415:0.762061:0.407143:0.752763:0.407143:0.000000
 :@0.404229:0.435204:0.408372:0.435204:0.408372:0.418706:0.404229:0.418706:0.000000
Observaciones:@0.404229:0.453017:0.517103:0.453017:0.517103:0.436072:0.404229:0.436072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.517105:0.452772:0.520457:0.452772:0.520457:0.436057:0.517105:0.436057:0.000000
i):@0.404229:0.470122:0.414768:0.470122:0.414768:0.453408:0.404229:0.453408:0.000000:0.000000
  Sean  ,  ,     :@0.414768:0.469906:0.531197:0.469906:0.531197:0.453408:0.414768:0.453408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α β γ:@0.466409:0.476467:0.508059:0.476467:0.508059:0.459195:0.466409:0.459195:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.512227:0.469387:0.526880:0.469387:0.526880:0.456014:0.512227:0.456014:0.000000
:@0.531059:0.468819:0.544363:0.468819:0.544363:0.455956:0.531059:0.455956:0.000000
+:@0.544546:0.462295:0.550847:0.462295:0.550847:0.452677:0.544546:0.452677:0.000000
. Aplicando la propiedad asociativa del produc-:@0.550960:0.469906:0.891763:0.469906:0.891763:0.453408:0.550960:0.453408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
to de números reales y la propiedad i) del teorema precedente, :@0.427971:0.487256:0.895826:0.487256:0.895826:0.470759:0.427971:0.470759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
obtenemos::@0.427971:0.504607:0.514008:0.504607:0.514008:0.488109:0.427971:0.488109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404236:0.521958:0.408378:0.521958:0.408378:0.505460:0.404236:0.505460:0.000000
log:@0.427971:0.522073:0.447063:0.522073:0.447063:0.505605:0.427971:0.505605:0.000000:0.000000:0.000000
(:@0.446678:0.521958:0.452631:0.521958:0.452631:0.505460:0.446678:0.505460:0.000000
αβγ:@0.452254:0.528519:0.478990:0.528519:0.478990:0.511248:0.452254:0.511248:0.000000:0.000000:0.000000
) = :@0.478659:0.521958:0.502191:0.521958:0.502191:0.505460:0.478659:0.505460:0.000000:0.000000:0.000000:0.000000
log:@0.501459:0.522073:0.520551:0.522073:0.520551:0.505605:0.501459:0.505605:0.000000:0.000000:0.000000
a:@0.520349:0.525302:0.525583:0.525302:0.525583:0.515701:0.520349:0.515701:0.000000
( ( )) = :@0.525358:0.521958:0.592836:0.521958:0.592836:0.505460:0.525358:0.505460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α βγ:@0.530926:0.528519:0.564071:0.528519:0.564071:0.511248:0.530926:0.511248:0.000000:0.000000:0.000000:0.000000
log:@0.592104:0.522073:0.611194:0.522073:0.611194:0.505605:0.592104:0.505605:0.000000:0.000000:0.000000
a:@0.610994:0.525302:0.616228:0.525302:0.616228:0.515701:0.610994:0.515701:0.000000
( ) + :@0.616003:0.521958:0.654387:0.521958:0.654387:0.505460:0.616003:0.505460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.621570:0.528519:0.631186:0.528519:0.631186:0.511248:0.621570:0.511248:0.000000
log:@0.653655:0.522073:0.672747:0.522073:0.672747:0.505605:0.653655:0.505605:0.000000:0.000000:0.000000
a:@0.672544:0.525302:0.677778:0.525302:0.677778:0.515701:0.672544:0.515701:0.000000
( ) = :@0.677555:0.521958:0.723775:0.521958:0.723775:0.505460:0.677555:0.505460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
βγ:@0.683122:0.528519:0.700578:0.528519:0.700578:0.511248:0.683122:0.511248:0.000000:0.000000
log:@0.723043:0.522073:0.742135:0.522073:0.742135:0.505605:0.723043:0.505605:0.000000:0.000000:0.000000
a:@0.741933:0.525302:0.747167:0.525302:0.747167:0.515701:0.741933:0.515701:0.000000
( ) + :@0.746942:0.521958:0.785327:0.521958:0.785327:0.505460:0.746942:0.505460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.752508:0.528519:0.762124:0.528519:0.762124:0.511248:0.752508:0.511248:0.000000
log:@0.784595:0.522073:0.803687:0.522073:0.803687:0.505605:0.784595:0.505605:0.000000:0.000000:0.000000
a:@0.803484:0.525302:0.808718:0.525302:0.808718:0.515701:0.803484:0.515701:0.000000
( ) + :@0.808493:0.521958:0.846558:0.521958:0.846558:0.505460:0.808493:0.505460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
β:@0.814060:0.528519:0.823358:0.528519:0.823358:0.511248:0.814060:0.511248:0.000000
log:@0.845826:0.522073:0.864918:0.522073:0.864918:0.505605:0.845826:0.505605:0.000000:0.000000:0.000000
a:@0.864716:0.525302:0.869950:0.525302:0.869950:0.515701:0.864716:0.515701:0.000000
( ).:@0.869725:0.521958:0.891771:0.521958:0.891771:0.505460:0.869725:0.505460:0.000000:0.000000:0.000000:0.000000
γ:@0.875292:0.528519:0.883785:0.528519:0.883785:0.511248:0.875292:0.511248:0.000000
 :@0.404245:0.556659:0.408387:0.556659:0.408387:0.540162:0.404245:0.540162:0.000000
De manera general, sean  , …     :@0.427979:0.556659:0.684335:0.556659:0.684335:0.540162:0.427979:0.540162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.604659:0.563221:0.614274:0.563221:0.614274:0.545949:0.604659:0.545949:0.000000
1:@0.614782:0.559936:0.619735:0.559936:0.619735:0.550318:0.614782:0.550318:0.000000
α:@0.645819:0.563221:0.655435:0.563221:0.655435:0.545949:0.645819:0.545949:0.000000
n:@0.655941:0.560003:0.661400:0.560003:0.661400:0.550402:0.655941:0.550402:0.000000
:@0.665542:0.556141:0.680194:0.556141:0.680194:0.542767:0.665542:0.542767:0.000000
:@0.684336:0.555572:0.697641:0.555572:0.697641:0.542710:0.684336:0.542710:0.000000
+:@0.697641:0.549049:0.703942:0.549049:0.703942:0.539431:0.697641:0.539431:0.000000
. Entonces,:@0.703942:0.556659:0.778845:0.556659:0.778845:0.540162:0.703942:0.540162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.504643:0.574126:0.524505:0.574126:0.524505:0.557657:0.504643:0.557657:0.000000:0.000000:0.000000
( × … ×  ) = :@0.524505:0.574010:0.635250:0.574010:0.635250:0.557512:0.524505:0.557512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.530462:0.580572:0.540078:0.580572:0.540078:0.563300:0.530462:0.563300:0.000000
1:@0.540584:0.577287:0.545537:0.577287:0.545537:0.567669:0.540584:0.567669:0.000000
α:@0.594625:0.580572:0.604241:0.580572:0.604241:0.563300:0.594625:0.563300:0.000000
n:@0.604747:0.577354:0.610206:0.577354:0.610206:0.567753:0.604747:0.567753:0.000000
log:@0.635250:0.574126:0.654342:0.574126:0.654342:0.557657:0.635250:0.557657:0.000000:0.000000:0.000000
a:@0.654148:0.577354:0.659382:0.577354:0.659382:0.567753:0.654148:0.567753:0.000000
( )  + … + :@0.659157:0.574010:0.739205:0.574010:0.739205:0.557512:0.659157:0.557512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.664724:0.580572:0.674340:0.580572:0.674340:0.563300:0.664724:0.563300:0.000000
1:@0.674010:0.577287:0.678963:0.577287:0.678963:0.567669:0.674010:0.567669:0.000000
log:@0.738819:0.574126:0.757911:0.574126:0.757911:0.557657:0.738819:0.557657:0.000000:0.000000:0.000000
a:@0.757717:0.577354:0.762951:0.577354:0.762951:0.567753:0.757717:0.567753:0.000000
( ). :@0.762726:0.574010:0.795501:0.574010:0.795501:0.557512:0.762726:0.557512:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.768294:0.580572:0.777910:0.580572:0.777910:0.563300:0.768294:0.563300:0.000000
n:@0.777578:0.577354:0.783037:0.577354:0.783037:0.567753:0.777578:0.567753:0.000000
 :@0.404243:0.591361:0.408385:0.591361:0.408385:0.574863:0.404243:0.574863:0.000000
ii):@0.404243:0.608928:0.419039:0.608928:0.419039:0.592214:0.404243:0.592214:0.000000:0.000000:0.000000
  Sea     :@0.419039:0.608712:0.488798:0.608712:0.488798:0.592214:0.419039:0.592214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.456241:0.615273:0.465857:0.615273:0.465857:0.598001:0.456241:0.598001:0.000000
:@0.470003:0.608193:0.484655:0.608193:0.484655:0.594820:0.470003:0.594820:0.000000
:@0.488797:0.607625:0.502102:0.607625:0.502102:0.594762:0.488797:0.594762:0.000000
+:@0.502102:0.601101:0.508403:0.601101:0.508403:0.591483:0.502102:0.591483:0.000000
. Puesto que :@0.508403:0.608712:0.598697:0.608712:0.598697:0.592214:0.508403:0.592214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.598697:0.608827:0.617789:0.608827:0.617789:0.592359:0.598697:0.592359:0.000000:0.000000:0.000000
a:@0.617596:0.612056:0.622830:0.612056:0.622830:0.602455:0.617596:0.602455:0.000000
(1) = 0, se sigue que::@0.622605:0.608712:0.765571:0.608712:0.765571:0.592214:0.622605:0.592214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.515240:0.635085:0.535103:0.635085:0.535103:0.618616:0.515240:0.618616:0.000000:0.000000:0.000000
a:@0.535295:0.638317:0.540529:0.638317:0.540529:0.628716:0.535295:0.628716:0.000000
         = :@0.540304:0.634973:0.592532:0.634973:0.592532:0.618475:0.540304:0.618475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.592532:0.635089:0.611624:0.635089:0.611624:0.618620:0.592532:0.618620:0.000000:0.000000:0.000000
a:@0.611430:0.638317:0.616664:0.638317:0.616664:0.628716:0.611430:0.628716:0.000000
(1) – :@0.616439:0.634973:0.655239:0.634973:0.655239:0.618475:0.616439:0.618475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.655239:0.635089:0.674331:0.635089:0.674331:0.618620:0.655239:0.618620:0.000000:0.000000:0.000000
a:@0.674137:0.638317:0.679371:0.638317:0.679371:0.628716:0.674137:0.628716:0.000000
( ) = – :@0.679146:0.634973:0.733685:0.634973:0.733685:0.618475:0.679146:0.618475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.684713:0.641534:0.694329:0.641534:0.694329:0.624263:0.684713:0.624263:0.000000
log:@0.733685:0.635089:0.752777:0.635089:0.752777:0.618620:0.733685:0.618620:0.000000:0.000000:0.000000
a:@0.752582:0.638317:0.757816:0.638317:0.757816:0.628716:0.752582:0.628716:0.000000
( ).:@0.757591:0.634973:0.780766:0.634973:0.780766:0.618475:0.757591:0.618475:0.000000:0.000000:0.000000:0.000000
α:@0.763160:0.641534:0.772776:0.641534:0.772776:0.624263:0.763160:0.624263:0.000000
iii):@0.404227:0.669891:0.423280:0.669891:0.423280:0.653177:0.404227:0.653177:0.000000:0.000000:0.000000:0.000000
 Para   = 1 y :@0.423280:0.669674:0.520936:0.669674:0.520936:0.653177:0.423280:0.653177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.462447:0.669790:0.477242:0.669790:0.477242:0.653321:0.462447:0.653321:0.000000
n:@0.520936:0.669790:0.530299:0.669790:0.530299:0.653321:0.520936:0.653321:0.000000
 :@0.530315:0.673019:0.532730:0.673019:0.532730:0.663417:0.530315:0.663417:0.000000
:@0.532730:0.669156:0.547383:0.669156:0.547383:0.655782:0.532730:0.655782:0.000000
   con   ≠ 0,     :@0.547382:0.669674:0.675453:0.669674:0.675453:0.653177:0.547382:0.653177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Z:@0.551525:0.668587:0.563816:0.668587:0.563816:0.655725:0.551525:0.655725:0.000000
n:@0.599052:0.669790:0.608415:0.669790:0.608415:0.653321:0.599052:0.653321:0.000000
α:@0.642898:0.676236:0.652513:0.676236:0.652513:0.658964:0.642898:0.658964:0.000000
:@0.656660:0.669156:0.671312:0.669156:0.671312:0.655782:0.656660:0.655782:0.000000
:@0.675454:0.668587:0.688759:0.668587:0.688759:0.655725:0.675454:0.655725:0.000000
+:@0.688759:0.662064:0.695060:0.662064:0.695060:0.652446:0.688759:0.652446:0.000000
, se tiene::@0.695059:0.669674:0.758982:0.669674:0.758982:0.653177:0.695059:0.653177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.573708:0.701397:0.593570:0.701397:0.593570:0.684929:0.573708:0.684929:0.000000:0.000000:0.000000
a:@0.593753:0.704626:0.598987:0.704626:0.598987:0.695025:0.593753:0.695025:0.000000
(    ) =      :@0.598988:0.701280:0.672740:0.701280:0.672740:0.684783:0.598988:0.684783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.604940:0.707842:0.614556:0.707842:0.614556:0.690570:0.604940:0.690570:0.000000
log:@0.672740:0.701396:0.692603:0.701396:0.692603:0.684927:0.672740:0.684927:0.000000:0.000000:0.000000
a:@0.692795:0.704626:0.698028:0.704626:0.698028:0.695025:0.692795:0.695025:0.000000
( ).:@0.698028:0.701280:0.722307:0.701280:0.722307:0.684783:0.698028:0.684783:0.000000:0.000000:0.000000:0.000000
α:@0.703980:0.707842:0.713596:0.707842:0.713596:0.690570:0.703980:0.690570:0.000000
Para  = 1, :@0.427973:0.735982:0.506305:0.735982:0.506305:0.719484:0.427973:0.719484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.462457:0.736098:0.471820:0.736098:0.471820:0.719629:0.462457:0.719629:0.000000
m:@0.506305:0.736098:0.521101:0.736098:0.521101:0.719629:0.506305:0.719629:0.000000
 :@0.521106:0.739327:0.523521:0.739327:0.523521:0.729726:0.521106:0.729726:0.000000
:@0.523522:0.735463:0.538174:0.735463:0.538174:0.722090:0.523522:0.722090:0.000000
  ,     :@0.538173:0.735982:0.594060:0.735982:0.594060:0.719484:0.538173:0.719484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Z:@0.542316:0.734895:0.554607:0.734895:0.554607:0.722033:0.542316:0.722033:0.000000
α:@0.561503:0.742543:0.571119:0.742543:0.571119:0.725272:0.561503:0.725272:0.000000
:@0.575265:0.735463:0.589917:0.735463:0.589917:0.722090:0.575265:0.722090:0.000000
:@0.594059:0.734895:0.607364:0.734895:0.607364:0.722033:0.594059:0.722033:0.000000
+:@0.607364:0.728373:0.613665:0.728373:0.613665:0.718755:0.607364:0.718755:0.000000
, se tiene :@0.613665:0.735982:0.678974:0.735982:0.678974:0.719484:0.613665:0.719484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.678974:0.736098:0.698836:0.736098:0.698836:0.719629:0.678974:0.719629:0.000000:0.000000:0.000000
a:@0.699026:0.739327:0.704260:0.739327:0.704260:0.729726:0.699026:0.729726:0.000000
( ) = :@0.704260:0.735982:0.754341:0.735982:0.754341:0.719484:0.704260:0.719484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.710214:0.742543:0.719830:0.742543:0.719830:0.725272:0.710214:0.725272:0.000000
m:@0.720671:0.729698:0.729297:0.729698:0.729297:0.720096:0.720671:0.720096:0.000000
mlog:@0.754341:0.736098:0.790350:0.736098:0.790350:0.719629:0.754341:0.719629:0.000000:0.000000:0.000000:0.000000
a:@0.790540:0.739327:0.795774:0.739327:0.795774:0.729726:0.790540:0.729726:0.000000
( ).:@0.795773:0.735982:0.820052:0.735982:0.820052:0.719484:0.795773:0.719484:0.000000:0.000000:0.000000:0.000000
α:@0.801725:0.742543:0.811341:0.742543:0.811341:0.725272:0.801725:0.725272:0.000000
Ejemplos resueltos:@0.404231:0.771059:0.534578:0.771059:0.534578:0.754272:0.404231:0.754272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.404231:0.788251:0.416503:0.788251:0.416503:0.771536:0.404231:0.771536:0.000000:0.000000
  Se conoce que :@0.416503:0.788034:0.536348:0.788034:0.536348:0.771536:0.416503:0.771536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.536348:0.788150:0.556211:0.788150:0.556211:0.771681:0.536348:0.771681:0.000000:0.000000:0.000000
(2)   0,301 0, :@0.556215:0.788034:0.653701:0.788034:0.653701:0.771536:0.556215:0.771536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≃:@0.580770:0.794596:0.593284:0.794596:0.593284:0.777324:0.580770:0.777324:0.000000
log:@0.653701:0.788150:0.673564:0.788150:0.673564:0.771681:0.653701:0.771681:0.000000:0.000000:0.000000
(3)   0,477 1. Calcular el valor:@0.673564:0.788034:0.883794:0.788034:0.883794:0.771536:0.673564:0.771536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≃:@0.698105:0.794596:0.710619:0.794596:0.710619:0.777324:0.698105:0.777324:0.000000
 :@0.404244:0.812513:0.408386:0.812513:0.408386:0.796015:0.404244:0.796015:0.000000
aproximado de :@0.427979:0.812513:0.540102:0.812513:0.540102:0.796015:0.427979:0.796015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.540102:0.812629:0.559965:0.812629:0.559965:0.796160:0.540102:0.796160:0.000000:0.000000:0.000000
(  144 ) con cuatro cifras luego de la coma :@0.559965:0.812513:0.861655:0.812513:0.861655:0.796015:0.559965:0.796015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
decimal.:@0.427979:0.829864:0.486795:0.829864:0.486795:0.813366:0.427979:0.813366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404244:0.854343:0.408386:0.854343:0.408386:0.837845:0.404244:0.837845:0.000000
Como 144 = 2  × 3 , entonces,:@0.427979:0.854343:0.642305:0.854343:0.642305:0.837845:0.427979:0.837845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.530199:0.847990:0.535152:0.847990:0.535152:0.838372:0.530199:0.838372:0.000000
2:@0.562741:0.847990:0.567694:0.847990:0.567694:0.838372:0.562741:0.838372:0.000000
 :@0.404227:0.878822:0.408369:0.878822:0.408369:0.862324:0.404227:0.862324:0.000000
log:@0.427962:0.878938:0.447824:0.878938:0.447824:0.862469:0.427962:0.862469:0.000000:0.000000:0.000000
(  144 ) = :@0.447824:0.878822:0.517353:0.878822:0.517353:0.862324:0.447824:0.862324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.517353:0.878938:0.537215:0.878938:0.537215:0.862469:0.517353:0.862469:0.000000:0.000000:0.000000
    2  × 3  = :@0.537215:0.878822:0.616569:0.878821:0.616569:0.862324:0.537215:0.862324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.559983:0.872470:0.564936:0.872470:0.564936:0.862851:0.559983:0.862851:0.000000
2:@0.592523:0.872470:0.597476:0.872470:0.597476:0.862851:0.592523:0.862851:0.000000
log:@0.616569:0.878937:0.636431:0.878937:0.636431:0.862468:0.616569:0.862468:0.000000:0.000000:0.000000
(2  × 3  ):@0.636431:0.878821:0.700635:0.878821:0.700635:0.862324:0.636431:0.862324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.650878:0.872470:0.658123:0.872470:0.658123:0.862851:0.650878:0.862851:0.000000:0.000000:0.000000
  :@0.685710:0.872470:0.690540:0.872470:0.690540:0.862851:0.685710:0.862851:0.000000:0.000000
 :@0.404239:0.906857:0.408381:0.906857:0.408381:0.890360:0.404239:0.890360:0.000000
=     :@0.427973:0.906857:0.459491:0.906857:0.459491:0.890360:0.427973:0.890360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.459491:0.906973:0.479354:0.906973:0.479354:0.890504:0.459491:0.890504:0.000000:0.000000:0.000000
(2) +      :@0.479354:0.906857:0.539558:0.906857:0.539558:0.890360:0.479354:0.890360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.539558:0.906973:0.559420:0.906973:0.559420:0.890504:0.539558:0.890504:0.000000:0.000000:0.000000
(3) =      × 0,301 0 +      × 0,477 1 = 0,431 64.:@0.559420:0.906857:0.865484:0.906857:0.865484:0.890360:0.559420:0.890360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α:@0.463811:0.192865:0.473427:0.192865:0.473427:0.175593:0.463811:0.175593:0.000000
β:@0.463979:0.207953:0.473276:0.207953:0.473276:0.190681:0.463979:0.190681:0.000000
m:@0.470329:0.212960:0.479207:0.212960:0.479207:0.203079:0.470329:0.203079:0.000000
n:@0.471959:0.222763:0.477577:0.222763:0.477577:0.212882:0.471959:0.212882:0.000000
m:@0.508377:0.218279:0.523173:0.218279:0.523173:0.201811:0.508377:0.201811:0.000000
n:@0.511094:0.234618:0.520457:0.234618:0.520457:0.218149:0.511094:0.218149:0.000000
1:@0.554021:0.626761:0.562517:0.626761:0.562517:0.610264:0.554021:0.610264:0.000000
α:@0.553458:0.648411:0.563074:0.648411:0.563074:0.631139:0.553458:0.631139:0.000000
1:@0.618305:0.687168:0.623403:0.687168:0.623403:0.677270:0.618305:0.677270:0.000000
n:@0.618051:0.697041:0.623668:0.697041:0.623668:0.687160:0.618051:0.687160:0.000000
1:@0.656258:0.692096:0.664754:0.692096:0.664754:0.675598:0.656258:0.675598:0.000000
n:@0.655834:0.708550:0.665197:0.708550:0.665197:0.692081:0.655834:0.692081:0.000000
5:@0.567180:0.801355:0.572133:0.801355:0.572133:0.791737:0.567180:0.791737:0.000000
5:@0.454825:0.868201:0.459778:0.868201:0.459778:0.858583:0.454825:0.858583:0.000000
5:@0.541938:0.868201:0.546891:0.868201:0.546891:0.858583:0.541938:0.858583:0.000000
4:@0.652971:0.862688:0.658068:0.862688:0.658068:0.852789:0.652971:0.852789:0.000000
5:@0.652971:0.872491:0.658068:0.872491:0.658068:0.862592:0.652971:0.862592:0.000000
2:@0.687425:0.862688:0.692523:0.862688:0.692523:0.852789:0.687425:0.852789:0.000000
5:@0.687425:0.872491:0.692523:0.872491:0.692523:0.862592:0.687425:0.862592:0.000000
4:@0.445966:0.898214:0.454462:0.898214:0.454462:0.881716:0.445966:0.881716:0.000000
5:@0.445966:0.914553:0.454462:0.914553:0.454462:0.898055:0.445966:0.898055:0.000000
4:@0.603147:0.898214:0.611643:0.898214:0.611643:0.881716:0.603147:0.881716:0.000000
5:@0.603147:0.914553:0.611643:0.914553:0.611643:0.898055:0.603147:0.898055:0.000000
2:@0.523756:0.898214:0.532252:0.898214:0.532252:0.881716:0.523756:0.881716:0.000000
5:@0.523756:0.914553:0.532252:0.914553:0.532252:0.898055:0.523756:0.898055:0.000000
2:@0.705288:0.898214:0.713784:0.898214:0.713784:0.881716:0.705288:0.881716:0.000000
5:@0.705288:0.914553:0.713784:0.914553:0.713784:0.898055:0.705288:0.898055:0.000000
Shutterstock, 423235870:@0.386147:0.731660:0.386147:0.663487:0.374678:0.663487:0.374678:0.731660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199646:0.097614:0.297269:0.097614:0.297269:0.082141:0.199646:0.082141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199646:0.110182:0.283709:0.110182:0.283709:0.094709:0.199646:0.094709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una curiosidad sobre :@0.199884:0.134655:0.341517:0.134655:0.341517:0.119592:0.199884:0.119592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las aplicaciones de logaritmos :@0.153341:0.150497:0.349466:0.150497:0.349466:0.135434:0.153341:0.135434:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en la vida real es la de Benjamin :@0.153341:0.166339:0.361079:0.166339:0.361079:0.151276:0.153341:0.151276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Franklin, el famoso científico. En :@0.153341:0.182181:0.363733:0.182181:0.363733:0.167118:0.153341:0.167118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
su testamento, Franklin donaba :@0.153341:0.198023:0.361218:0.198023:0.361218:0.182960:0.153341:0.182960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 000 libras a los habitantes de :@0.153341:0.213865:0.354268:0.213865:0.354268:0.198802:0.153341:0.198802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Boston, a condición de que se :@0.153341:0.229707:0.350908:0.229707:0.350908:0.214644:0.153341:0.214644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
prestasen al 5 % a artesanos :@0.153341:0.245549:0.336555:0.245549:0.336555:0.230486:0.153341:0.230486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
jóvenes. Según Franklin, al cabo :@0.153341:0.261391:0.360530:0.261391:0.360530:0.246328:0.153341:0.246328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de 100 años, la suma se habría :@0.153341:0.277233:0.351701:0.277233:0.351701:0.262170:0.153341:0.262170:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
convertido en 131 000 libras. :@0.153341:0.293075:0.342570:0.293075:0.342570:0.278012:0.153341:0.278012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Comprobemos si esto es cierto.:@0.153341:0.308917:0.356818:0.308917:0.356818:0.293854:0.153341:0.293854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El capital final al cabo de esos :@0.153341:0.331888:0.348287:0.331888:0.348287:0.316825:0.153341:0.316825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
100 años será: :@0.153341:0.347730:0.246601:0.347730:0.246601:0.332667:0.153341:0.332667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.153341:0.370806:0.160165:0.370806:0.160165:0.355770:0.153341:0.355770:0.000000
 = 1 000 · 1,05 . Para calcular :@0.160165:0.370701:0.353099:0.370699:0.353099:0.355636:0.160165:0.355638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
100:@0.248278:0.364899:0.261845:0.364899:0.261845:0.356117:0.248278:0.356117:0.000000:0.000000:0.000000
esa enorme potencia, usaremos :@0.153349:0.386541:0.362018:0.386541:0.362018:0.371478:0.153349:0.371478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los logaritmos::@0.153349:0.402383:0.247156:0.402383:0.247156:0.387320:0.153349:0.387320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.153349:0.425460:0.160174:0.425460:0.160174:0.410423:0.153349:0.410423:0.000000
 = 1 000 · 1,05 ; :@0.160174:0.425354:0.268141:0.425353:0.268141:0.410290:0.160174:0.410291:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
100:@0.248278:0.419554:0.261845:0.419554:0.261845:0.410772:0.248278:0.410772:0.000000:0.000000:0.000000
log x log:@0.153349:0.441301:0.217656:0.441301:0.217656:0.426264:0.153349:0.426264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   = :@0.171484:0.441195:0.199523:0.441195:0.199523:0.426132:0.171484:0.426132:0.000000:0.000000:0.000000:0.000000:0.000000
 1 000 + 100 · :@0.217658:0.441195:0.307033:0.441195:0.307033:0.426132:0.217658:0.426132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.307033:0.441301:0.325168:0.441301:0.325168:0.426264:0.307033:0.426264:0.000000:0.000000:0.000000
 1,05;:@0.325168:0.441195:0.357252:0.441195:0.357252:0.426132:0.325168:0.426132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log x:@0.153349:0.457143:0.182091:0.457143:0.182091:0.442106:0.153349:0.442106:0.000000:0.000000:0.000000:0.000000:0.000000
   = 3 + 100 · 0,021 2 = 5,12;:@0.171484:0.457037:0.348880:0.457037:0.348880:0.441974:0.171484:0.441974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.153349:0.472985:0.160174:0.472985:0.160174:0.457948:0.153349:0.457948:0.000000
 = 10  = 131 825,67 libras:@0.160174:0.472879:0.331684:0.472879:0.331684:0.457816:0.160174:0.457816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5,12:@0.193116:0.467080:0.208150:0.467080:0.208150:0.458298:0.193116:0.458298:0.000000:0.000000:0.000000:0.000000
Adaptado de: :@0.281114:0.494019:0.364920:0.494019:0.364920:0.480391:0.281114:0.480391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
https://docs.google.com/presen-:@0.169663:0.508353:0.361500:0.508353:0.361500:0.494724:0.169663:0.494724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tation/d/1Dxguaru5WCw4hHw-:@0.169313:0.522686:0.361500:0.522686:0.361500:0.509057:0.169313:0.509057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
QWNPj6INmEEkztPs38hikZeiM-:@0.169536:0.537019:0.361498:0.537019:0.361498:0.523391:0.169536:0.523391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cO4/htmlpresent?hl=es:@0.222835:0.551352:0.361498:0.551352:0.361498:0.537724:0.222835:0.537724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.153346:0.749565:0.164826:0.749565:0.164826:0.739541:0.153346:0.739541:0.000000
 :@0.164826:0.750273:0.167707:0.750273:0.167707:0.738796:0.164826:0.738796:0.000000
Benjamin Franklin (1706 - 1790).:@0.167707:0.750273:0.326413:0.750273:0.326413:0.738796:0.167707:0.738796:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga escribe:@0.153346:0.777564:0.261014:0.777564:0.261014:0.762303:0.153346:0.762303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.198745:0.777366:0.213451:0.777366:0.213451:0.762303:0.198745:0.762303:0.000000:0.000000:0.000000
 otras aplica-:@0.261014:0.777366:0.343615:0.777366:0.343615:0.762303:0.261014:0.762303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciones de los logaritmos en la :@0.153346:0.793208:0.347624:0.793208:0.347624:0.778145:0.153346:0.778145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vida cotidiana.:@0.153346:0.809050:0.246889:0.809050:0.246889:0.793987:0.153346:0.793987:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000