50:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
Inecuación exponencial:@0.115209:0.214277:0.354736:0.214277:0.354736:0.192767:0.115209:0.192767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las inecuaciones exponenciales en una incógnita tienen la siguiente forma:  :@0.115209:0.233495:0.675365:0.233495:0.675365:0.217106:0.115209:0.217106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.115209:0.257214:0.124478:0.257214:0.124478:0.240852:0.115209:0.240852:0.000000
f x:@0.124478:0.251171:0.134415:0.251171:0.134415:0.241633:0.124478:0.241633:0.000000:0.000000:0.000000
( ):@0.127217:0.251171:0.137262:0.251171:0.137262:0.241617:0.127217:0.241617:0.000000:0.000000:0.000000
 > :@0.137262:0.257219:0.156316:0.257219:0.156316:0.240830:0.137262:0.240830:0.000000:0.000000:0.000000
a:@0.156316:0.257219:0.165585:0.257219:0.165585:0.240857:0.156316:0.240857:0.000000
g x:@0.165585:0.251171:0.178187:0.251171:0.178187:0.241633:0.165585:0.241633:0.000000:0.000000:0.000000
( ):@0.170989:0.251171:0.181034:0.251171:0.181034:0.241617:0.170989:0.241617:0.000000:0.000000:0.000000
a:@0.115209:0.277379:0.124478:0.277379:0.124478:0.261018:0.115209:0.261018:0.000000
f x:@0.124478:0.271332:0.134415:0.271332:0.134415:0.261794:0.124478:0.261794:0.000000:0.000000:0.000000
( ):@0.127217:0.271332:0.137262:0.271332:0.137262:0.261777:0.127217:0.261777:0.000000:0.000000:0.000000
 < :@0.137262:0.277379:0.156316:0.277379:0.156316:0.260991:0.137262:0.260991:0.000000:0.000000:0.000000
a:@0.156316:0.277379:0.165585:0.277379:0.165585:0.261018:0.156316:0.261018:0.000000
g x:@0.165585:0.271332:0.178187:0.271332:0.178187:0.261794:0.165585:0.261794:0.000000:0.000000:0.000000
( ):@0.170989:0.271332:0.181034:0.271332:0.181034:0.261777:0.170989:0.261777:0.000000:0.000000:0.000000
Condiciones para resolución :@0.115209:0.310054:0.364462:0.310054:0.364462:0.291617:0.115209:0.291617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a)  :@0.115209:0.329901:0.137746:0.329901:0.137746:0.313000:0.115209:0.313000:0.000000:0.000000:0.000000:0.000000
Cuando a > 1 se cumple que::@0.148452:0.329901:0.363079:0.329901:0.363079:0.313512:0.148452:0.313512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.115209:0.384060:0.119023:0.384060:0.119023:0.367160:0.115209:0.367160:0.000000
a:@0.151434:0.356462:0.160703:0.356462:0.160703:0.340101:0.151434:0.340101:0.000000
a:@0.197982:0.356462:0.207251:0.356462:0.207251:0.340101:0.197982:0.340101:0.000000
a:@0.151434:0.379047:0.160703:0.379047:0.160703:0.362686:0.151434:0.362686:0.000000
a:@0.197982:0.379047:0.207251:0.379047:0.207251:0.362686:0.197982:0.362686:0.000000
a:@0.151434:0.422392:0.160703:0.422392:0.160703:0.406030:0.151434:0.406030:0.000000
a:@0.197982:0.422392:0.207251:0.422392:0.207251:0.406030:0.197982:0.406030:0.000000
a:@0.151434:0.444976:0.160703:0.444976:0.160703:0.428615:0.151434:0.428615:0.000000
a:@0.197982:0.444976:0.207251:0.444976:0.207251:0.428615:0.197982:0.428615:0.000000
f x:@0.161276:0.348801:0.175182:0.348801:0.175182:0.339319:0.161276:0.339319:0.000000:0.000000:0.000000
gx:@0.208236:0.348801:0.223027:0.348801:0.223027:0.339319:0.208236:0.339319:0.000000:0.000000
f x:@0.161276:0.371397:0.175182:0.371397:0.175182:0.361914:0.161276:0.361914:0.000000:0.000000:0.000000
gx:@0.208236:0.371397:0.223027:0.371397:0.223027:0.361914:0.208236:0.361914:0.000000:0.000000
f x:@0.161276:0.414730:0.175182:0.414730:0.175182:0.405248:0.161276:0.405248:0.000000:0.000000:0.000000
gx:@0.208236:0.414730:0.223027:0.414730:0.223027:0.405248:0.208236:0.405248:0.000000:0.000000
f x:@0.161276:0.437326:0.175182:0.437326:0.175182:0.427843:0.161276:0.427843:0.000000:0.000000:0.000000
gx:@0.208236:0.437326:0.223027:0.437326:0.223027:0.427843:0.208236:0.427843:0.000000:0.000000
>:@0.184572:0.357057:0.194689:0.357057:0.194689:0.339036:0.184572:0.339036:0.000000
⇔:@0.237717:0.357057:0.256919:0.357057:0.256919:0.339036:0.237717:0.339036:0.000000
<:@0.184572:0.379642:0.194689:0.379642:0.194689:0.361621:0.184572:0.361621:0.000000
⇔:@0.237717:0.379642:0.256919:0.379642:0.256919:0.361621:0.237717:0.361621:0.000000
>:@0.184572:0.422986:0.194689:0.422986:0.194689:0.404965:0.184572:0.404965:0.000000
⇔:@0.237717:0.422986:0.256919:0.422986:0.256919:0.404965:0.237717:0.404965:0.000000
<:@0.184572:0.445571:0.194689:0.445571:0.194689:0.427550:0.184572:0.427550:0.000000
⇔:@0.237717:0.445571:0.256919:0.445571:0.256919:0.427550:0.237717:0.427550:0.000000
f(x) > g(x) ó:@0.264511:0.356461:0.344789:0.356461:0.344789:0.340072:0.264511:0.340072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x) < g(x):@0.264511:0.379046:0.331440:0.379046:0.331440:0.362657:0.264511:0.362657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x) < g(x) ó:@0.264511:0.422390:0.344789:0.422390:0.344789:0.406001:0.264511:0.406001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x) > g(x):@0.264511:0.444975:0.331440:0.444975:0.331440:0.428586:0.264511:0.428586:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.166092:0.348801:0.179816:0.348801:0.179816:0.339303:0.166092:0.339303:0.000000:0.000000
():@0.213946:0.348801:0.227669:0.348801:0.227669:0.339303:0.213946:0.339303:0.000000:0.000000
():@0.166092:0.371397:0.179816:0.371397:0.179816:0.361898:0.166092:0.361898:0.000000:0.000000
():@0.213946:0.371397:0.227669:0.371397:0.227669:0.361898:0.213946:0.361898:0.000000:0.000000
():@0.166092:0.414730:0.179816:0.414730:0.179816:0.405232:0.166092:0.405232:0.000000:0.000000
():@0.213946:0.414730:0.227669:0.414730:0.227669:0.405232:0.213946:0.405232:0.000000:0.000000
():@0.166092:0.437326:0.179816:0.437326:0.179816:0.427827:0.166092:0.427827:0.000000:0.000000
():@0.213946:0.437326:0.227669:0.437326:0.227669:0.427827:0.213946:0.427827:0.000000:0.000000
Inecuaciones con funciones exponenciales  :@0.115891:0.141978:0.763052:0.141978:0.763052:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y logarítmicas :@0.115891:0.178453:0.334756:0.178453:0.334756:0.137716:0.115891:0.137716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.77. Aplicar las propiedades de los exponentes y los logaritmos para resolver ecuaciones e inecuaciones con funciones exponenciales y logarítmicas, con :@0.125388:0.069719:0.877793:0.069719:0.877793:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ayuda de las TIC.:@0.125388:0.080280:0.201844:0.080280:0.201844:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
13:@0.048440:0.122645:0.082072:0.122645:0.082072:0.065614:0.048440:0.065614:0.000000:0.000000
Actividad resuelta:@0.115209:0.569043:0.272331:0.569043:0.272331:0.550606:0.115209:0.550606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Inecuaciones exponenciales:@0.205489:0.597992:0.407840:0.597992:0.407840:0.582628:0.205489:0.582628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Inecuaciones logarítmicas:@0.594631:0.597992:0.782391:0.597992:0.782391:0.582628:0.594631:0.582628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea la inecuación 2    2 , :@0.122464:0.619140:0.304231:0.619138:0.304231:0.604239:0.122464:0.604241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.249841:0.613640:0.253797:0.613640:0.253797:0.604969:0.249841:0.604969:0.000000
+2:@0.253797:0.613640:0.264384:0.613640:0.264384:0.604954:0.253797:0.604954:0.000000:0.000000
≤:@0.268051:0.619138:0.278035:0.619138:0.278035:0.604264:0.268051:0.604264:0.000000
x:@0.289879:0.613640:0.293835:0.613640:0.293835:0.604969:0.289879:0.604969:0.000000
2:@0.293835:0.611596:0.297647:0.611596:0.297647:0.604648:0.293835:0.604648:0.000000
determinamos:@0.304231:0.619138:0.406521:0.619138:0.406521:0.604025:0.304231:0.604025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el conjunto :@0.406521:0.619138:0.490015:0.619138:0.490015:0.604239:0.406521:0.604239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
solución.:@0.122468:0.634225:0.181855:0.634225:0.181855:0.619326:0.122468:0.619326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Encontramos:@0.504255:0.619138:0.596443:0.619138:0.596443:0.604025:0.504255:0.604025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la solución de la siguiente inecuación::@0.596443:0.619138:0.852400:0.619138:0.852400:0.604239:0.596443:0.604239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log 1 – 2x    2.:@0.635929:0.634225:0.741097:0.634225:0.741097:0.619326:0.635929:0.619326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.657511:0.637101:0.662277:0.637101:0.662277:0.628415:0.657511:0.628415:0.000000
(:@0.662277:0.634841:0.667855:0.634841:0.667855:0.620684:0.662277:0.620684:0.000000
):@0.707106:0.634841:0.712685:0.634841:0.712685:0.620684:0.707106:0.620684:0.000000
≤:@0.716353:0.634225:0.726338:0.634225:0.726338:0.619351:0.716353:0.619351:0.000000
{:@0.148643:0.773848:0.049267:0.773848:0.049267:0.739302:0.148643:0.739302:0.000000
}:@0.255980:0.773848:0.156604:0.773848:0.156604:0.739302:0.255980:0.739302:0.000000
]:@0.278684:0.769027:0.284206:0.769027:0.284206:0.746645:0.278684:0.746645:0.000000
][:@0.324999:0.769027:0.351302:0.769027:0.351302:0.746645:0.324999:0.746645:0.000000:0.000000
[:@0.376311:0.769027:0.381833:0.769027:0.381833:0.746645:0.376311:0.746645:0.000000
≤:@0.154627:0.664491:0.163732:0.664491:0.163732:0.648272:0.154627:0.648272:0.000000
+ ≤:@0.137478:0.684817:0.168874:0.684817:0.168874:0.668598:0.137478:0.668598:0.000000:0.000000:0.000000
− −≥:@0.144029:0.705144:0.198562:0.705144:0.198562:0.688925:0.144029:0.688925:0.000000:0.000000:0.000000:0.000000
−:@0.142238:0.723814:0.151343:0.723814:0.151343:0.707596:0.142238:0.707596:0.000000
+ ≥:@0.183236:0.723814:0.215908:0.723814:0.215908:0.707596:0.183236:0.707596:0.000000:0.000000:0.000000
≥:@0.141641:0.742485:0.150746:0.742485:0.150746:0.726267:0.141641:0.726267:0.000000
≤ −:@0.186216:0.742485:0.207385:0.742485:0.207385:0.726267:0.186216:0.726267:0.000000:0.000000:0.000000
=:@0.136981:0.766596:0.146086:0.766596:0.146086:0.750377:0.136981:0.750377:0.000000
∈:@0.168210:0.766596:0.123580:0.766596:0.123580:0.750377:0.168210:0.750377:0.000000
≤:@0.224657:0.766596:0.180027:0.766596:0.180027:0.750377:0.224657:0.750377:0.000000
= −∞ − ∪:@0.266310:0.766596:0.344552:0.766596:0.344552:0.750377:0.266310:0.750377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∞:@0.364653:0.766596:0.376478:0.766596:0.376478:0.750377:0.364653:0.750377:0.000000
+:@0.139831:0.657370:0.145108:0.657370:0.145108:0.647970:0.139831:0.647970:0.000000
+:@0.209843:0.759495:0.215120:0.759495:0.215120:0.750096:0.209843:0.750096:0.000000
2:@0.125934:0.663956:0.134027:0.663956:0.134027:0.649205:0.125934:0.649205:0.000000
2:@0.166359:0.663956:0.174453:0.663956:0.174453:0.649205:0.166359:0.649205:0.000000
2:@0.149070:0.684282:0.157163:0.684282:0.157163:0.669532:0.149070:0.669532:0.000000
20:@0.178756:0.704608:0.209273:0.704608:0.209273:0.689858:0.178756:0.689858:0.000000:0.000000
(:@0.125569:0.723279:0.129964:0.723279:0.129964:0.708529:0.125569:0.708529:0.000000
2)(:@0.153838:0.723279:0.170953:0.723279:0.170953:0.708529:0.153838:0.708529:0.000000:0.000000:0.000000
1) 0:@0.193791:0.723279:0.226615:0.723279:0.226615:0.708529:0.193791:0.708529:0.000000:0.000000:0.000000:0.000000
2,:@0.153365:0.741950:0.164493:0.741950:0.164493:0.727200:0.153365:0.727200:0.000000:0.000000
1:@0.207216:0.741950:0.215310:0.741950:0.215310:0.727200:0.207216:0.727200:0.000000
2:@0.195955:0.766061:0.204048:0.766061:0.204048:0.751311:0.195955:0.751311:0.000000
2:@0.236381:0.766061:0.244474:0.766061:0.244474:0.751311:0.236381:0.751311:0.000000
, 1:@0.305500:0.766061:0.326974:0.766061:0.326974:0.751311:0.305500:0.751311:0.000000:0.000000:0.000000
2,:@0.351956:0.766061:0.363084:0.766061:0.363084:0.751311:0.351956:0.751311:0.000000:0.000000
2:@0.145581:0.657060:0.150271:0.657060:0.150271:0.648511:0.145581:0.648511:0.000000
2:@0.181009:0.677395:0.185700:0.677395:0.185700:0.668847:0.181009:0.668847:0.000000
2:@0.135450:0.697731:0.140141:0.697731:0.140141:0.689183:0.135450:0.689183:0.000000
1:@0.133989:0.743769:0.138680:0.743769:0.138680:0.735221:0.133989:0.735221:0.000000
2:@0.177146:0.743769:0.181836:0.743769:0.181836:0.735221:0.177146:0.735221:0.000000
2:@0.215592:0.759185:0.220283:0.759185:0.220283:0.750637:0.215592:0.750637:0.000000
2:@0.179975:0.653338:0.183355:0.653338:0.183355:0.647179:0.179975:0.647179:0.000000
2:@0.249989:0.755459:0.253369:0.755459:0.253369:0.749300:0.249989:0.749300:0.000000
x:@0.127252:0.684289:0.133969:0.684289:0.133969:0.669563:0.127252:0.669563:0.000000
x:@0.172811:0.684289:0.179528:0.684289:0.179528:0.669563:0.172811:0.669563:0.000000
x:@0.127252:0.704615:0.133969:0.704615:0.133969:0.689890:0.127252:0.689890:0.000000
x:@0.156939:0.704615:0.163656:0.704615:0.163656:0.689890:0.156939:0.689890:0.000000
x:@0.132012:0.723286:0.138729:0.723286:0.138729:0.708561:0.132012:0.708561:0.000000
x:@0.173010:0.723286:0.179727:0.723286:0.179727:0.708561:0.173010:0.708561:0.000000
x:@0.127252:0.741957:0.133969:0.741957:0.133969:0.727232:0.127252:0.727232:0.000000
x:@0.169792:0.741957:0.176509:0.741957:0.176509:0.727232:0.169792:0.727232:0.000000
S:@0.126257:0.766067:0.133521:0.766067:0.133521:0.751342:0.126257:0.751342:0.000000
x:@0.157818:0.766067:0.164535:0.766067:0.164535:0.751342:0.157818:0.751342:0.000000
x:@0.134884:0.657060:0.138777:0.657060:0.138777:0.648526:0.134884:0.648526:0.000000
x:@0.175311:0.657060:0.179204:0.657060:0.179204:0.648526:0.175311:0.648526:0.000000
x:@0.204896:0.759185:0.208789:0.759185:0.208789:0.750651:0.204896:0.750651:0.000000
x:@0.245323:0.759185:0.249216:0.759185:0.249216:0.750651:0.245323:0.750651:0.000000
:@0.179928:0.766864:0.191903:0.766864:0.191903:0.751790:0.179928:0.751790:0.000000
La representación gráfica de la solución de la :@0.122474:0.790878:0.424920:0.790878:0.424920:0.775979:0.122474:0.775979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inecuación es::@0.122474:0.805965:0.216874:0.805965:0.216874:0.791066:0.122474:0.791066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Primero :@0.504261:0.658345:0.560064:0.658345:0.560064:0.643446:0.504261:0.643446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
evaluamos:@0.560064:0.658345:0.635582:0.658345:0.635582:0.643233:0.560064:0.643233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la existencia del logaritmo:  :@0.635582:0.658345:0.823825:0.658345:0.823825:0.643446:0.635582:0.643446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 – 2  > 0       < :@0.504261:0.678990:0.623924:0.678990:0.623924:0.664091:0.504261:0.664091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.536325:0.678990:0.543110:0.678990:0.543110:0.664116:0.536325:0.664116:0.000000
⇒:@0.575945:0.679606:0.592480:0.679606:0.592480:0.665449:0.575945:0.665449:0.000000
x:@0.599817:0.678990:0.606602:0.678990:0.606602:0.664116:0.599817:0.664116:0.000000
 1 :@0.623912:0.670286:0.639425:0.670286:0.639425:0.655387:0.623912:0.655387:0.000000:0.000000:0.000000
 2:@0.623912:0.689988:0.635756:0.689988:0.635756:0.675089:0.623912:0.675089:0.000000:0.000000
.:@0.641954:0.678987:0.644869:0.678987:0.644869:0.664088:0.641954:0.664088:0.000000
Luego :@0.504250:0.706232:0.550185:0.706232:0.550185:0.691333:0.504250:0.691333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolvemos:@0.550185:0.706232:0.629757:0.706232:0.629757:0.691119:0.550185:0.691119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la inecuación: log 1 – 2x    2:@0.629757:0.706232:0.830528:0.706230:0.830528:0.691331:0.629757:0.691333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.749857:0.709106:0.754623:0.709106:0.754623:0.700420:0.749857:0.700420:0.000000
(:@0.754623:0.706846:0.760201:0.706846:0.760201:0.692689:0.754623:0.692689:0.000000
):@0.799452:0.706846:0.805031:0.706846:0.805031:0.692689:0.799452:0.692689:0.000000
≤:@0.808699:0.706230:0.818684:0.706230:0.818684:0.691356:0.808699:0.691356:0.000000
1 – 2    9:@0.504258:0.724876:0.568604:0.724876:0.568604:0.709976:0.504258:0.709976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x ≤:@0.536322:0.724876:0.556760:0.724876:0.556760:0.710002:0.536322:0.710002:0.000000:0.000000:0.000000
x   –4:@0.504258:0.743521:0.545318:0.743521:0.545318:0.728622:0.504258:0.728622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≥:@0.515114:0.743521:0.525098:0.743521:0.525098:0.728647:0.515114:0.728647:0.000000
=:@0.516693:0.770076:0.525798:0.770076:0.525798:0.756060:0.516693:0.756060:0.000000
∈:@0.547923:0.770076:0.559748:0.770076:0.559748:0.756060:0.547923:0.756060:0.000000
−:@0.613449:0.770076:0.622555:0.770076:0.622555:0.756060:0.613449:0.756060:0.000000
≤:@0.649721:0.770076:0.658826:0.770076:0.658826:0.756060:0.649721:0.756060:0.000000
= −:@0.679656:0.770076:0.708647:0.770076:0.708647:0.756060:0.679656:0.756060:0.000000:0.000000:0.000000
log (1 2 ) 2:@0.574978:0.769466:0.669562:0.769466:0.669562:0.754716:0.574978:0.754716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4,:@0.708487:0.769466:0.720262:0.769466:0.720262:0.754716:0.708487:0.754716:0.000000:0.000000
1:@0.723528:0.761400:0.731622:0.761400:0.731622:0.746650:0.723528:0.746650:0.000000
2:@0.722815:0.778900:0.730908:0.778900:0.730908:0.764150:0.722815:0.764150:0.000000
3:@0.595895:0.771269:0.600586:0.771269:0.600586:0.762721:0.595895:0.762721:0.000000
S:@0.505999:0.769466:0.513263:0.769466:0.513263:0.754741:0.505999:0.754741:0.000000
x:@0.537560:0.769466:0.544277:0.769466:0.544277:0.754741:0.537560:0.754741:0.000000
x:@0.634283:0.769466:0.640999:0.769466:0.640999:0.754741:0.634283:0.754741:0.000000
:@0.559667:0.770250:0.571642:0.770250:0.571642:0.755176:0.559667:0.755176:0.000000
La representación gráfica de la solución de la inecuación :@0.504253:0.798855:0.874598:0.798855:0.874598:0.783956:0.504253:0.783956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logarítmica es la sola  intersección de las dos soluciones::@0.504253:0.813943:0.855371:0.813943:0.855371:0.799044:0.504253:0.799044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b)  :@0.509247:0.330033:0.533092:0.330033:0.533092:0.313132:0.509247:0.313132:0.000000:0.000000:0.000000:0.000000
Cuando 0< a < 1 se cumple que::@0.542490:0.330033:0.781128:0.330033:0.781128:0.313644:0.542490:0.313644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.509247:0.384192:0.513061:0.384192:0.513061:0.367292:0.509247:0.367292:0.000000
a:@0.545471:0.356594:0.554740:0.356594:0.554740:0.340233:0.545471:0.340233:0.000000
a:@0.592019:0.356594:0.601288:0.356594:0.601288:0.340233:0.592019:0.340233:0.000000
a:@0.545471:0.379179:0.554740:0.379179:0.554740:0.362818:0.545471:0.362818:0.000000
a:@0.592019:0.379179:0.601288:0.379179:0.601288:0.362818:0.592019:0.362818:0.000000
a:@0.545471:0.422524:0.554740:0.422524:0.554740:0.406162:0.545471:0.406162:0.000000
a:@0.592019:0.422524:0.601288:0.422524:0.601288:0.406162:0.592019:0.406162:0.000000
a:@0.545471:0.445108:0.554740:0.445108:0.554740:0.428747:0.545471:0.428747:0.000000
a:@0.592019:0.445108:0.601288:0.445108:0.601288:0.428747:0.592019:0.428747:0.000000
f x:@0.555313:0.348932:0.569219:0.348932:0.569219:0.339450:0.555313:0.339450:0.000000:0.000000:0.000000
gx:@0.602272:0.348932:0.617063:0.348932:0.617063:0.339450:0.602272:0.339450:0.000000:0.000000
f x:@0.555313:0.371527:0.569219:0.371527:0.569219:0.362045:0.555313:0.362045:0.000000:0.000000:0.000000
gx:@0.602272:0.371527:0.617063:0.371527:0.617063:0.362045:0.602272:0.362045:0.000000:0.000000
f x:@0.555313:0.414863:0.569219:0.414863:0.569219:0.405380:0.555313:0.405380:0.000000:0.000000:0.000000
gx:@0.602272:0.414863:0.617063:0.414863:0.617063:0.405380:0.602272:0.405380:0.000000:0.000000
f x:@0.555313:0.437458:0.569219:0.437458:0.569219:0.427975:0.555313:0.427975:0.000000:0.000000:0.000000
gx:@0.602272:0.437458:0.617063:0.437458:0.617063:0.427975:0.602272:0.427975:0.000000:0.000000
>:@0.578610:0.357189:0.588727:0.357189:0.588727:0.339168:0.578610:0.339168:0.000000
⇔:@0.631756:0.357189:0.650957:0.357189:0.650957:0.339168:0.631756:0.339168:0.000000
<:@0.578610:0.379774:0.588727:0.379774:0.588727:0.361753:0.578610:0.361753:0.000000
⇔:@0.631756:0.379774:0.650957:0.379774:0.650957:0.361753:0.631756:0.361753:0.000000
>:@0.578610:0.423118:0.588727:0.423118:0.588727:0.405097:0.578610:0.405097:0.000000
⇔:@0.631756:0.423118:0.650957:0.423118:0.650957:0.405097:0.631756:0.405097:0.000000
<:@0.578610:0.445703:0.588727:0.445703:0.588727:0.427682:0.578610:0.427682:0.000000
⇔:@0.631756:0.445703:0.650957:0.445703:0.650957:0.427682:0.631756:0.427682:0.000000
f(x) > g(x) ó:@0.658549:0.356593:0.738827:0.356593:0.738827:0.340204:0.658549:0.340204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x) < g(x):@0.658549:0.379178:0.725478:0.379178:0.725478:0.362789:0.658549:0.362789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x) < g(x) ó:@0.658549:0.422522:0.738827:0.422522:0.738827:0.406133:0.658549:0.406133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x) > g(x):@0.658549:0.445107:0.725478:0.445107:0.725478:0.428718:0.658549:0.428718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.560129:0.348932:0.573852:0.348932:0.573852:0.339434:0.560129:0.339434:0.000000:0.000000
():@0.607982:0.348932:0.621706:0.348932:0.621706:0.339434:0.607982:0.339434:0.000000:0.000000
():@0.560129:0.371527:0.573852:0.371527:0.573852:0.362029:0.560129:0.362029:0.000000:0.000000
():@0.607982:0.371527:0.621706:0.371527:0.621706:0.362029:0.607982:0.362029:0.000000:0.000000
():@0.560129:0.414863:0.573852:0.414863:0.573852:0.405364:0.560129:0.405364:0.000000:0.000000
():@0.607982:0.414863:0.621706:0.414863:0.621706:0.405364:0.607982:0.405364:0.000000:0.000000
():@0.560129:0.437458:0.573852:0.437458:0.573852:0.427959:0.560129:0.427959:0.000000:0.000000
():@0.607982:0.437458:0.621706:0.437458:0.621706:0.427959:0.607982:0.427959:0.000000:0.000000
Inecuación logarítmica:@0.115354:0.416271:0.346557:0.416271:0.346557:0.394761:0.115354:0.394761:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una inecuación logarítmica es una desigualdad en la que la variable aparece en el argumento del logarit-:@0.115354:0.435489:0.879898:0.435489:0.879898:0.419100:0.115354:0.419100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mo. Para su resolución es necesario considerar las características de la base, la definición y las propiedades :@0.115354:0.452085:0.883950:0.452085:0.883950:0.435696:0.115354:0.435696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la monotonía del logaritmo.:@0.115354:0.468682:0.342637:0.468682:0.342637:0.452293:0.115354:0.452293:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Propiedades de la monotonía del logaritmo::@0.115354:0.492401:0.438092:0.492401:0.438092:0.476012:0.115354:0.476012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.115354:0.527115:0.119390:0.527115:0.119390:0.510726:0.115354:0.510726:0.000000
Si   > 1,    > :@0.119390:0.512676:0.212744:0.512676:0.212744:0.496287:0.119390:0.496287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.135827:0.512676:0.145096:0.512676:0.145096:0.496315:0.135827:0.496315:0.000000
b:@0.184421:0.512676:0.193690:0.512676:0.193690:0.496315:0.184421:0.496315:0.000000
c:@0.212744:0.512676:0.220410:0.512676:0.220410:0.496315:0.212744:0.496315:0.000000
⇒:@0.119390:0.537072:0.137578:0.537072:0.137578:0.521500:0.119390:0.521500:0.000000
 log  > log:@0.137578:0.536395:0.222806:0.536396:0.222806:0.520007:0.137578:0.520006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.165344:0.539560:0.170747:0.539560:0.170747:0.530021:0.165344:0.530021:0.000000
b:@0.170748:0.536396:0.180017:0.536396:0.180017:0.520035:0.170748:0.520035:0.000000
a:@0.222804:0.539560:0.228208:0.539560:0.228208:0.530021:0.222804:0.530021:0.000000
c:@0.228209:0.536396:0.235875:0.536396:0.235875:0.520035:0.228209:0.520035:0.000000
Si 0 <   < 1,    > :@0.283657:0.512677:0.399604:0.512677:0.399604:0.496288:0.283657:0.496288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.326096:0.512677:0.335365:0.512677:0.335365:0.496316:0.326096:0.496316:0.000000
b c:@0.371963:0.512677:0.406588:0.512677:0.406588:0.496316:0.371963:0.496316:0.000000:0.000000:0.000000
⇒:@0.283657:0.537074:0.301846:0.537074:0.301846:0.521501:0.283657:0.521501:0.000000
 log  > log:@0.301846:0.536396:0.387072:0.536396:0.387072:0.520007:0.301846:0.520007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.329609:0.539560:0.335013:0.539560:0.335013:0.530021:0.329609:0.530021:0.000000
b:@0.335014:0.536396:0.344283:0.536396:0.344283:0.520035:0.335014:0.520035:0.000000
a:@0.387072:0.539560:0.392475:0.539560:0.392475:0.530021:0.387072:0.530021:0.000000
c:@0.392474:0.536396:0.400140:0.536396:0.400140:0.520035:0.392474:0.520035:0.000000
0:@0.302755:0.870372:0.307658:0.870372:0.307658:0.861750:0.302755:0.861750:0.000000
x:@0.474099:0.858533:0.478937:0.858533:0.478937:0.847925:0.474099:0.847925:0.000000
10:@0.465676:0.872076:0.475482:0.872076:0.475482:0.863453:0.465676:0.863453:0.000000:0.000000
8:@0.436525:0.872076:0.441428:0.872076:0.441428:0.863453:0.436525:0.863453:0.000000
6:@0.403284:0.872076:0.408187:0.872076:0.408187:0.863453:0.403284:0.863453:0.000000
4:@0.369985:0.872076:0.374888:0.872076:0.374888:0.863453:0.369985:0.863453:0.000000
2:@0.336706:0.872076:0.341609:0.872076:0.341609:0.863453:0.336706:0.863453:0.000000
–2:@0.267791:0.872076:0.277473:0.872076:0.277473:0.863453:0.267791:0.863453:0.000000:0.000000
–4:@0.235429:0.872076:0.245111:0.872076:0.245111:0.863453:0.235429:0.863453:0.000000:0.000000
–6:@0.202188:0.872076:0.211870:0.872076:0.211870:0.863453:0.202188:0.863453:0.000000:0.000000
–8:@0.168889:0.872076:0.178571:0.872076:0.178571:0.863453:0.168889:0.863453:0.000000:0.000000
–10:@0.132399:0.872076:0.146984:0.872076:0.146984:0.863453:0.132399:0.863453:0.000000:0.000000:0.000000
0:@0.752418:0.870480:0.757321:0.870480:0.757321:0.861858:0.752418:0.861858:0.000000
x:@0.856303:0.856937:0.861142:0.856937:0.861142:0.846330:0.856303:0.846330:0.000000
2:@0.836711:0.870480:0.841614:0.870480:0.841614:0.861858:0.836711:0.861858:0.000000
–2:@0.668061:0.870480:0.677743:0.870480:0.677743:0.861858:0.668061:0.861858:0.000000:0.000000
–4:@0.582406:0.870480:0.592088:0.870480:0.592088:0.861858:0.582406:0.861858:0.000000:0.000000
2:@0.774695:0.877016:0.779598:0.877016:0.779598:0.868393:0.774695:0.868393:0.000000
1:@0.774695:0.869986:0.779598:0.869986:0.779598:0.861364:0.774695:0.861364:0.000000