124:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000 5.:@0.404236:0.096411:0.416508:0.096411:0.416508:0.079697:0.404236:0.079697:0.000000:0.000000 Considera la ecuación: solución de:@0.416508:0.096194:0.749526:0.096194:0.749526:0.079697:0.416508:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.590568:0.096310:0.598043:0.096310:0.598043:0.079841:0.590568:0.079841:0.000000 :@0.602193:0.095676:0.616845:0.095676:0.616845:0.082302:0.602193:0.082302:0.000000 ӏ:@0.620987:0.103781:0.625981:0.103781:0.625981:0.084782:0.620987:0.084782:0.000000 :@0.630132:0.095826:0.645482:0.095826:0.645482:0.081816:0.630132:0.081816:0.000000 :@0.649624:0.095107:0.662928:0.095107:0.662928:0.082245:0.649624:0.082245:0.000000 ln x:@0.526145:0.120789:0.552654:0.120789:0.552654:0.104320:0.526145:0.104320:0.000000:0.000000:0.000000:0.000000 ( + 10) – (2 – 5) = – ( ),:@0.539226:0.120673:0.769857:0.120674:0.769857:0.104176:0.539226:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ln x:@0.634185:0.120789:0.669190:0.120789:0.669190:0.104320:0.634185:0.104320:0.000000:0.000000:0.000000:0.000000 ln:@0.732014:0.120789:0.745095:0.120789:0.745095:0.104320:0.732014:0.104320:0.000000:0.000000 α:@0.751048:0.127748:0.761144:0.127748:0.761144:0.109612:0.751048:0.109612:0.000000 con ≥ . Estudia la existencia de soluciones de esta ecuación.:@0.427976:0.145153:0.882617:0.145152:0.882617:0.128655:0.427976:0.128655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α:@0.459073:0.152226:0.469170:0.152226:0.469170:0.134091:0.459073:0.134091:0.000000 :@0.404230:0.179854:0.408372:0.179854:0.408372:0.163356:0.404230:0.163356:0.000000 Primeramente, determinamos el conjunto en el que esta ecua-:@0.427965:0.179854:0.891699:0.179854:0.891699:0.163356:0.427965:0.163356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 I:@0.735766:0.179969:0.739773:0.179969:0.739773:0.163501:0.735766:0.163501:0.000000 ción tiene sentido. Como el dominio de la función logaritmo na-:@0.427965:0.197205:0.891676:0.197205:0.891676:0.180707:0.427965:0.180707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tural es ]0, ∞[, se sigue que ( + 10) y (2 – 5) están bien :@0.427965:0.214555:0.895878:0.214555:0.895878:0.198058:0.427965:0.198058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ln:@0.466130:0.214671:0.483218:0.214671:0.483218:0.198202:0.466130:0.198202:0.000000:0.000000 ln x:@0.651673:0.214671:0.678240:0.214671:0.678240:0.198202:0.651673:0.198202:0.000000:0.000000:0.000000:0.000000 ln x:@0.741315:0.214671:0.776358:0.214671:0.776358:0.198202:0.741315:0.198202:0.000000:0.000000:0.000000:0.000000 definidos, si y solo si, se verifica que sus argumentos son positivos, :@0.427984:0.231906:0.895910:0.231906:0.895910:0.215408:0.427984:0.215408:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 esto es,:@0.427984:0.249257:0.479211:0.249257:0.479211:0.232759:0.427984:0.232759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.423245:0.283958:0.427387:0.283958:0.427387:0.267461:0.423245:0.267461:0.000000 x:@0.446980:0.284074:0.454455:0.284074:0.454455:0.267605:0.446980:0.267605:0.000000 + 10 > 0, y:@0.454455:0.283958:0.536987:0.283958:0.536987:0.267461:0.454455:0.267461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 – 5 > 0:@0.446980:0.301309:0.517818:0.301309:0.517818:0.284811:0.446980:0.284811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.455476:0.301425:0.462951:0.301425:0.462951:0.284956:0.455476:0.284956:0.000000 :@0.404250:0.336011:0.408392:0.336011:0.408392:0.319513:0.404250:0.319513:0.000000 Por lo tanto, ( + 10) – (2 – 5) está bien definido, si y solo:@0.427984:0.336011:0.889747:0.336011:0.889747:0.319513:0.427984:0.319513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ln x:@0.519456:0.336126:0.545965:0.336126:0.545965:0.319657:0.519456:0.319657:0.000000:0.000000:0.000000:0.000000 ln x:@0.627495:0.336126:0.662500:0.336126:0.662500:0.319657:0.627495:0.319657:0.000000:0.000000:0.000000:0.000000 si, > . Así, = , ∞ . Para , ∞ , tenemos: :@0.427984:0.367618:0.807775:0.367618:0.807775:0.351120:0.427984:0.351120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.444938:0.367734:0.452413:0.367734:0.452413:0.351265:0.444938:0.351265:0.000000 ӏ:@0.522627:0.375204:0.527621:0.375204:0.527621:0.356205:0.522627:0.356205:0.000000 x:@0.641354:0.367734:0.648829:0.367734:0.648829:0.351265:0.641354:0.351265:0.000000 :@0.652967:0.367099:0.667620:0.367099:0.667620:0.353726:0.652967:0.353726:0.000000 :@0.404245:0.402782:0.408387:0.402782:0.408387:0.386284:0.404245:0.386284:0.000000 ln x:@0.427980:0.402898:0.454489:0.402898:0.454489:0.386429:0.427980:0.386429:0.000000:0.000000:0.000000:0.000000 ( + 10) – (2 – 5) = :@0.441061:0.402782:0.623349:0.402782:0.623349:0.386284:0.441061:0.386284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ln x:@0.536020:0.402898:0.571025:0.402898:0.571025:0.386429:0.536020:0.386429:0.000000:0.000000:0.000000:0.000000 ln .:@0.623349:0.402898:0.713838:0.402898:0.713838:0.386429:0.623349:0.386429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404245:0.437484:0.408387:0.437484:0.408387:0.420986:0.404245:0.420986:0.000000 La ecuación propuesta se escribe en forma equivalente, como: :@0.427980:0.437484:0.872345:0.437484:0.872345:0.420986:0.427980:0.420986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ln = – ln:@0.537966:0.469206:0.672032:0.469206:0.672032:0.452738:0.537966:0.452738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.672032:0.469091:0.713122:0.469096:0.713122:0.452598:0.672032:0.452593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α:@0.677977:0.476170:0.688074:0.476170:0.688074:0.458034:0.677977:0.458034:0.000000 ln ,:@0.713122:0.469212:0.758048:0.469212:0.758048:0.452743:0.713122:0.452743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404242:0.503797:0.408384:0.503797:0.408384:0.487300:0.404242:0.487300:0.000000 y por la inyectividad de la función , se obtiene::@0.427977:0.503797:0.772517:0.503797:0.772517:0.487300:0.427977:0.487300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ln:@0.672470:0.503913:0.689558:0.503913:0.689558:0.487444:0.672470:0.487444:0.000000:0.000000 = ( + 10) = 2 – 5 .:@0.520912:0.538499:0.775100:0.538499:0.775100:0.522001:0.520912:0.522001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.610415:0.537578:0.627871:0.537578:0.627871:0.522176:0.610415:0.522176:0.000000 α:@0.632012:0.545573:0.642108:0.545573:0.642108:0.527437:0.632012:0.527437:0.000000 x:@0.648065:0.538615:0.655540:0.538615:0.655540:0.522146:0.648065:0.522146:0.000000 x:@0.733448:0.538615:0.740923:0.538615:0.740923:0.522146:0.733448:0.522146:0.000000 :@0.404244:0.555850:0.408386:0.555850:0.408386:0.539352:0.404244:0.539352:0.000000 :@0.404244:0.573200:0.408386:0.573200:0.408386:0.556703:0.404244:0.556703:0.000000 Elevando al cuadrado ambos miembros en la última igualdad, :@0.427979:0.573200:0.895945:0.573200:0.895945:0.556703:0.427979:0.556703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.891770:0.573200:0.895912:0.573200:0.895912:0.556703:0.891770:0.556703:0.000000 tenemos::@0.427979:0.590551:0.493247:0.590551:0.493247:0.574053:0.427979:0.574053:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α:@0.470298:0.622105:0.480394:0.622105:0.480394:0.603969:0.470298:0.603969:0.000000 2:@0.480399:0.608678:0.485352:0.608678:0.485352:0.599060:0.480399:0.599060:0.000000 ( + 10) = 2 – 5, + 20 + 100 = (2 – 5),:@0.485351:0.615031:0.825712:0.615031:0.825712:0.598533:0.485351:0.598533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.491304:0.615146:0.498779:0.615146:0.498779:0.598678:0.491304:0.598678:0.000000 2:@0.540815:0.608678:0.545768:0.608678:0.545768:0.599060:0.540815:0.599060:0.000000 x:@0.573357:0.615146:0.580832:0.615146:0.580832:0.598678:0.573357:0.598678:0.000000 x:@0.627434:0.615146:0.634909:0.615146:0.634909:0.598678:0.627434:0.598678:0.000000 2:@0.634907:0.608678:0.639860:0.608678:0.639860:0.599060:0.634907:0.599060:0.000000 x:@0.675944:0.615146:0.683419:0.615146:0.683419:0.598678:0.675944:0.598678:0.000000 x:@0.782250:0.615146:0.789725:0.615146:0.789725:0.598678:0.782250:0.598678:0.000000 x:@0.539893:0.649848:0.547368:0.649848:0.547368:0.633379:0.539893:0.633379:0.000000 2:@0.547362:0.643379:0.552315:0.643379:0.552315:0.633761:0.547362:0.633761:0.000000 + 20 – + 100 + = 0.:@0.552316:0.649732:0.756121:0.649732:0.756121:0.633235:0.552316:0.633235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.588399:0.649848:0.595874:0.649848:0.595874:0.633379:0.588399:0.633379:0.000000 x:@0.635368:0.649848:0.642843:0.649848:0.642843:0.633379:0.635368:0.633379:0.000000 :@0.404243:0.684434:0.408385:0.684434:0.408385:0.667936:0.404243:0.667936:0.000000 Determinemos las raíces de esta ecuación en términos de . Para :@0.427978:0.684434:0.895908:0.684434:0.895908:0.667936:0.427978:0.667936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α:@0.843945:0.691508:0.854041:0.691508:0.854041:0.673372:0.843945:0.673372:0.000000 el efecto, aplicamos la conocida fórmula de obtención de las raí-:@0.427974:0.701785:0.891778:0.701785:0.891778:0.685287:0.427974:0.685287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ces de una ecuación de segundo grado. Tenemos::@0.427974:0.719135:0.779058:0.719135:0.779058:0.702638:0.427974:0.702638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404240:0.771188:0.408382:0.771188:0.408382:0.754690:0.404240:0.754690:0.000000 x:@0.427974:0.771303:0.435449:0.771303:0.435449:0.754834:0.427974:0.754834:0.000000 = :@0.435449:0.771188:0.454541:0.771188:0.454541:0.754690:0.435449:0.754690:0.000000:0.000000:0.000000 =:@0.427974:0.840591:0.438782:0.840591:0.438782:0.824093:0.427974:0.824093:0.000000 :@0.404240:0.909994:0.408382:0.909994:0.408382:0.893496:0.404240:0.893496:0.000000 = = .:@0.427974:0.909994:0.833412:0.909994:0.833412:0.893496:0.427974:0.893496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Recuerda que…:@0.199250:0.155805:0.309010:0.155805:0.309010:0.140333:0.199250:0.140333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las ecuaciones logarít-:@0.199487:0.184433:0.345413:0.184433:0.345413:0.169370:0.199487:0.169370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 micas son aquellas ecuaciones :@0.152944:0.200275:0.352571:0.200275:0.352571:0.185212:0.152944:0.185212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en las que la incógnita aparece :@0.152944:0.216117:0.354348:0.216117:0.354348:0.201054:0.152944:0.201054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 afectada por un logaritmo.:@0.152944:0.231959:0.326010:0.231959:0.326010:0.216896:0.152944:0.216896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para resolver ecuaciones :@0.152944:0.254930:0.314207:0.254930:0.314207:0.239867:0.152944:0.239867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 logarítmicas, ten en cuenta lo :@0.152944:0.270772:0.347785:0.270772:0.347785:0.255709:0.152944:0.255709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 siguiente::@0.152944:0.286614:0.212996:0.286614:0.212996:0.271551:0.152944:0.271551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 •:@0.152944:0.310231:0.160032:0.310231:0.160032:0.294535:0.152944:0.294535:0.000000 Aplica las propiedades de :@0.160032:0.309585:0.339394:0.309585:0.339394:0.294521:0.160032:0.294521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los logaritmos hasta obtener :@0.169566:0.325427:0.357881:0.325427:0.357881:0.310363:0.169566:0.310363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 un solo logaritmo en ambos :@0.169566:0.341269:0.356564:0.341269:0.356564:0.326205:0.169566:0.326205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 miembros de la ecuación.:@0.169566:0.357111:0.334963:0.357111:0.334963:0.342047:0.169566:0.342047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 •:@0.152944:0.380728:0.160032:0.380728:0.160032:0.365032:0.152944:0.365032:0.000000 Resuelve la ecuación que :@0.160032:0.380081:0.334699:0.380081:0.334699:0.365018:0.160032:0.365018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 queda y verifica la validez de :@0.169566:0.395923:0.357602:0.395923:0.357602:0.380860:0.169566:0.380860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las soluciones obtenidas.:@0.169566:0.411765:0.328998:0.411765:0.328998:0.396702:0.169566:0.396702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.619034:0.113123:0.627530:0.113123:0.627530:0.096625:0.619034:0.096625:0.000000 2:@0.619034:0.129461:0.627530:0.129461:0.627530:0.112963:0.619034:0.112963:0.000000 2:@0.493851:0.137715:0.502347:0.137715:0.502347:0.121218:0.493851:0.121218:0.000000 10:@0.489498:0.154054:0.506682:0.154054:0.506682:0.137556:0.489498:0.137556:0.000000:0.000000 ⇔:@0.552741:0.293709:0.570197:0.293709:0.570197:0.278307:0.552741:0.278307:0.000000 x:@0.596058:0.280351:0.603533:0.280351:0.603533:0.263882:0.596058:0.263882:0.000000 > –10, y:@0.603533:0.280235:0.668977:0.280235:0.668977:0.263738:0.603533:0.263738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.596058:0.304830:0.603533:0.304830:0.603533:0.288361:0.596058:0.288361:0.000000 > .:@0.603533:0.304714:0.641948:0.304714:0.641948:0.288217:0.603533:0.288217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.625589:0.297382:0.634085:0.297382:0.634085:0.280885:0.625589:0.280885:0.000000 2:@0.625589:0.313721:0.634085:0.313721:0.634085:0.297223:0.625589:0.297223:0.000000 1:@0.611001:0.328532:0.619497:0.328532:0.619497:0.312034:0.611001:0.312034:0.000000 2:@0.611001:0.344871:0.619497:0.344871:0.619497:0.328373:0.611001:0.328373:0.000000 5:@0.474409:0.359911:0.482905:0.359911:0.482905:0.343413:0.474409:0.343413:0.000000 2:@0.474409:0.376249:0.482905:0.376249:0.482905:0.359752:0.474409:0.359752:0.000000 5:@0.552693:0.359911:0.561189:0.359911:0.561189:0.343413:0.552693:0.343413:0.000000 2:@0.552693:0.376249:0.561189:0.376249:0.561189:0.359752:0.552693:0.359752:0.000000 5:@0.680011:0.359911:0.688507:0.359911:0.688507:0.343413:0.680011:0.343413:0.000000 2:@0.680011:0.376249:0.688507:0.376249:0.688507:0.359752:0.680011:0.359752:0.000000 1:@0.520208:0.395390:0.528704:0.395390:0.528704:0.378893:0.520208:0.378893:0.000000 2:@0.520208:0.411729:0.528704:0.411729:0.528704:0.395231:0.520208:0.395231:0.000000 x:@0.651419:0.395593:0.658894:0.395593:0.658894:0.379124:0.651419:0.379124:0.000000 + 10:@0.658894:0.395477:0.694978:0.395477:0.694978:0.378979:0.658894:0.378979:0.000000:0.000000:0.000000:0.000000:0.000000 2 – 5:@0.649493:0.413074:0.696885:0.413074:0.696885:0.396576:0.649493:0.396576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.662131:0.413189:0.669606:0.413189:0.669606:0.396721:0.662131:0.396721:0.000000 x:@0.567657:0.462230:0.575132:0.462230:0.575132:0.445761:0.567657:0.445761:0.000000 + 10:@0.575132:0.462114:0.611216:0.462114:0.611216:0.445616:0.575132:0.445616:0.000000:0.000000:0.000000:0.000000:0.000000 2 – 5:@0.565731:0.479711:0.613123:0.479711:0.613123:0.463213:0.565731:0.463213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.578369:0.479826:0.585844:0.479826:0.585844:0.463358:0.578369:0.463358:0.000000 1:@0.737260:0.461615:0.745756:0.461615:0.745756:0.445117:0.737260:0.445117:0.000000 α :@0.736458:0.484531:0.750424:0.484531:0.750424:0.466395:0.736458:0.466395:0.000000:0.000000 1:@0.593535:0.530824:0.602031:0.530824:0.602031:0.514327:0.593535:0.514327:0.000000 α :@0.592732:0.553742:0.606699:0.553742:0.606699:0.535606:0.592732:0.535606:0.000000:0.000000 2:@0.620630:0.642200:0.629126:0.642200:0.629126:0.625702:0.620630:0.625702:0.000000 α:@0.617295:0.665619:0.627392:0.665619:0.627392:0.647483:0.617295:0.647483:0.000000 2:@0.627452:0.652193:0.632405:0.652193:0.632405:0.642575:0.627452:0.642575:0.000000 :@0.632461:0.665619:0.636331:0.665619:0.636331:0.647483:0.632461:0.647483:0.000000 5:@0.711329:0.642200:0.719825:0.642200:0.719825:0.625702:0.711329:0.625702:0.000000 α:@0.707996:0.665619:0.718092:0.665619:0.718092:0.647483:0.707996:0.647483:0.000000 2:@0.718151:0.652193:0.723104:0.652193:0.723104:0.642575:0.718151:0.642575:0.000000 :@0.723162:0.665619:0.727031:0.665619:0.727031:0.647483:0.723162:0.647483:0.000000 1:@0.753370:0.607273:0.761866:0.607273:0.761866:0.590776:0.753370:0.590776:0.000000 α:@0.750034:0.630692:0.760131:0.630692:0.760131:0.612557:0.750034:0.612557:0.000000 2:@0.760191:0.617265:0.765144:0.617265:0.765144:0.607647:0.760191:0.607647:0.000000 x:@0.513021:0.531471:0.520496:0.531471:0.520496:0.515002:0.513021:0.515002:0.000000 + 10:@0.520496:0.531355:0.556580:0.531355:0.556580:0.514857:0.520496:0.514857:0.000000:0.000000:0.000000:0.000000:0.000000 2 – 5:@0.511095:0.548951:0.558487:0.548951:0.558487:0.532454:0.511095:0.532454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.523733:0.549067:0.531208:0.549067:0.531208:0.532598:0.523733:0.532598:0.000000 2:@0.586281:0.781622:0.598919:0.781622:0.598919:0.765124:0.586281:0.765124:0.000000:0.000000 2:@0.584750:0.850773:0.597388:0.850773:0.597388:0.834276:0.584750:0.834276:0.000000:0.000000 2:@0.525391:0.920281:0.538029:0.920281:0.538029:0.903783:0.525391:0.903783:0.000000:0.000000 2:@0.727819:0.920281:0.740457:0.920281:0.740457:0.903783:0.727819:0.903783:0.000000:0.000000 2:@0.515710:0.747651:0.524206:0.747651:0.524206:0.731153:0.515710:0.731153:0.000000 α:@0.512375:0.771070:0.522471:0.771070:0.522471:0.752934:0.512375:0.752934:0.000000 2:@0.522532:0.757643:0.527485:0.757643:0.527485:0.748025:0.522532:0.748025:0.000000 :@0.527541:0.771070:0.531410:0.771070:0.531410:0.752934:0.527541:0.752934:0.000000 2:@0.501583:0.816802:0.510079:0.816802:0.510079:0.800305:0.501583:0.800305:0.000000 α:@0.498247:0.840221:0.508344:0.840221:0.508344:0.822086:0.498247:0.822086:0.000000 2:@0.508404:0.826794:0.513357:0.826794:0.513357:0.817176:0.508404:0.817176:0.000000 :@0.513413:0.840221:0.517283:0.840221:0.517283:0.822086:0.513413:0.822086:0.000000 2:@0.501583:0.886310:0.510079:0.886310:0.510079:0.869812:0.501583:0.869812:0.000000 α:@0.498247:0.909729:0.508344:0.909729:0.508344:0.891593:0.498247:0.891593:0.000000 2:@0.508404:0.896303:0.513357:0.896303:0.513357:0.886685:0.508404:0.886685:0.000000 :@0.513413:0.909729:0.517283:0.909729:0.517283:0.891593:0.513413:0.891593:0.000000 2:@0.699261:0.886310:0.707757:0.886310:0.707757:0.869812:0.699261:0.869812:0.000000 α:@0.695926:0.909729:0.706022:0.909729:0.706022:0.891593:0.695926:0.891593:0.000000 2:@0.706083:0.896303:0.711036:0.896303:0.711036:0.886685:0.706083:0.886685:0.000000 :@0.711092:0.909729:0.714961:0.909729:0.714961:0.891593:0.711092:0.891593:0.000000 2:@0.604498:0.747651:0.612994:0.747651:0.612994:0.731153:0.604498:0.731153:0.000000 α:@0.601162:0.771070:0.611259:0.771070:0.611259:0.752934:0.601162:0.752934:0.000000 2:@0.611319:0.757643:0.616272:0.757643:0.616272:0.748025:0.611319:0.748025:0.000000 :@0.616328:0.771070:0.620198:0.771070:0.620198:0.752934:0.616328:0.752934:0.000000 5:@0.706937:0.747651:0.715433:0.747651:0.715433:0.731153:0.706937:0.731153:0.000000 α:@0.703603:0.771070:0.713700:0.771070:0.713700:0.752934:0.703603:0.752934:0.000000 2:@0.713758:0.757643:0.718712:0.757643:0.718712:0.748025:0.713758:0.748025:0.000000 :@0.718769:0.771070:0.722639:0.771070:0.722639:0.752934:0.718769:0.752934:0.000000 – 20 – ± 20 – – 4 100 +:@0.456562:0.755133:0.699979:0.755133:0.699979:0.738635:0.456562:0.738635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – 20 + ± 400 – + – 400 –:@0.444830:0.824290:0.707338:0.824290:0.707338:0.807793:0.444830:0.807793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – 20 + ± –:@0.444830:0.893795:0.580438:0.893795:0.580438:0.877297:0.444830:0.877297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – 20 + ±:@0.642511:0.893795:0.728896:0.893795:0.728896:0.877297:0.642511:0.877297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.622729:0.741155:0.627682:0.741155:0.627682:0.731536:0.622729:0.731536:0.000000 80:@0.593914:0.816802:0.611098:0.816802:0.611098:0.800305:0.593914:0.800305:0.000000:0.000000 α:@0.594924:0.840221:0.605020:0.840221:0.605020:0.822086:0.594924:0.822086:0.000000 2:@0.605079:0.826794:0.610032:0.826794:0.610032:0.817176:0.605079:0.817176:0.000000 :@0.610088:0.840221:0.613958:0.840221:0.613958:0.822086:0.610088:0.822086:0.000000 100:@0.587616:0.886310:0.613490:0.886310:0.613490:0.869812:0.587616:0.869812:0.000000:0.000000:0.000000 α:@0.592970:0.909729:0.603067:0.909729:0.603067:0.891593:0.592970:0.891593:0.000000 2:@0.603127:0.896303:0.608081:0.896303:0.608081:0.886685:0.603127:0.886685:0.000000 :@0.608136:0.909729:0.612006:0.909729:0.612006:0.891593:0.608136:0.891593:0.000000 20:@0.712569:0.816802:0.729754:0.816802:0.729754:0.800305:0.712569:0.800305:0.000000:0.000000 α:@0.713579:0.840221:0.723676:0.840221:0.723676:0.822086:0.713579:0.822086:0.000000 2:@0.723736:0.826794:0.728689:0.826794:0.728689:0.817176:0.723736:0.817176:0.000000 :@0.728745:0.840221:0.732615:0.840221:0.732615:0.822086:0.728745:0.822086:0.000000 4:@0.635205:0.816802:0.643701:0.816802:0.643701:0.800305:0.635205:0.800305:0.000000 α:@0.631871:0.840221:0.641968:0.840221:0.641968:0.822086:0.631871:0.822086:0.000000 4:@0.642026:0.826794:0.646980:0.826794:0.646980:0.817176:0.642026:0.817176:0.000000 4:@0.551443:0.886310:0.559939:0.886310:0.559939:0.869812:0.551443:0.869812:0.000000 α:@0.548109:0.909729:0.558206:0.909729:0.558206:0.891593:0.548109:0.891593:0.000000 4:@0.558264:0.896303:0.563218:0.896303:0.563218:0.886685:0.558264:0.886685:0.000000 4 – 100:@0.748935:0.886310:0.802473:0.886310:0.802473:0.869812:0.748935:0.869812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 α:@0.802568:0.893384:0.812665:0.893384:0.812665:0.875248:0.802568:0.875248:0.000000 2:@0.812725:0.879958:0.817678:0.879958:0.817678:0.870340:0.812725:0.870340:0.000000 α:@0.775704:0.909729:0.785801:0.909729:0.785801:0.891593:0.775704:0.891593:0.000000 4:@0.785861:0.896303:0.790814:0.896303:0.790814:0.886685:0.785861:0.886685:0.000000 Interdisciplinariedad:@0.199644:0.565983:0.346429:0.565983:0.346429:0.550511:0.199644:0.550511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática y Estudios :@0.199880:0.595033:0.362358:0.595033:0.362358:0.579561:0.199880:0.579561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sociales:@0.153337:0.610875:0.209094:0.610875:0.209094:0.595403:0.153337:0.595403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las ecuaciones logarítmicas son :@0.153337:0.642137:0.363165:0.642137:0.363165:0.627074:0.153337:0.627074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ampliamente utilizadas para :@0.153337:0.657979:0.339403:0.657979:0.339403:0.642916:0.153337:0.642916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 resolver problemas de creci-:@0.153337:0.673821:0.335447:0.673821:0.335447:0.658758:0.153337:0.658758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 miento poblacional, que son :@0.153337:0.689663:0.342270:0.689663:0.342270:0.674600:0.153337:0.674600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 modelados mediante ecuacio-:@0.153337:0.705505:0.350572:0.705505:0.350572:0.690442:0.153337:0.690442:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 nes exponenciales.:@0.153337:0.721347:0.273563:0.721347:0.273563:0.706284:0.153337:0.706284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Indaga responde:@0.153344:0.877704:0.276560:0.877704:0.276560:0.862443:0.153344:0.862443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.198744:0.877506:0.213449:0.877506:0.213449:0.862443:0.198744:0.862443:0.000000:0.000000:0.000000 con tus :@0.276562:0.877506:0.332305:0.877506:0.332305:0.862443:0.276562:0.862443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 palabras: ¿qué es un logaritmo? :@0.153344:0.893348:0.358000:0.893348:0.358000:0.878285:0.153344:0.878285:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Escribe:@0.153344:0.909388:0.201470:0.909388:0.201470:0.894127:0.153344:0.894127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 otras aplicaciones.:@0.201470:0.909190:0.323156:0.909190:0.323156:0.894127:0.201470:0.894127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Shutterstock, 598826399:@0.386147:0.857253:0.386147:0.789080:0.374678:0.789080:0.374678:0.857253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000