POR FAVOOOR ME URGE AYUDA ES PARA HOY Y NO LO LOGRO :(

Adjuntos:

Respuestas

Respuesta dada por: roycroos

SOLUCIÓN

♛ HØlα!! ✌

Utilizaremos algunas propiedades de logaritmos

$1. \boxed{\mathtt{\log{m^n} = n\log{m}}}\\\\2. \boxed{\mathtt{\log{a\times b}= \log{a} + \log{b}}}\\\\3.\boxed{\mathtt{\dfrac{\log{m}}{\log{n}} = \log{m}-\log{n}}}$

En el problema 5

$\log{(m^6)}+\dfrac{2}{5}\log{(npm^{15})}-4\log{(p^3m^9)}\\\\\mathrm{Aplicamos \: la\: propiedad \:1}\\\\6\log (m) + \dfrac{2}{5}\log{(npm^{15})}-4\log{(p^3m^9)$

$\mathrm{Aplicamos \: la\: propiedad \:2}\\\\6\log (m) + \dfrac{2}{5}[\log{(n)}+\log{(p)+\log{m^{15}}]- 4[\log{(p^3)}+\log{(m^9)}]$

$6\log (m) + \dfrac{2}{5}\log{(n)}+\dfrac{2}{5}\log{(p)+\dfrac{2}{5}\log{m^{15}- 4\log{(p^3)}-4\log{(m^9)}$

$\mathrm{Aplicamos \: la\: propiedad \:1}$

$6\log (m) + \dfrac{2}{5}\log{(n)}+\dfrac{2}{5}\log{(p)+(15)\dfrac{2}{5}\log{m}- (3)4\log{(p)}-(9)4\log{(m)}$

$6\log (m) + \dfrac{2}{5}\log{(n)}+\dfrac{2}{5}\log{(p)+6\log{m}- 12\log{(p)}-36\log{(m)$

$\mathrm{Agrupamos}$

$[6\log (m)+6\log{(m)}-36\log{(m)]+ \dfrac{2}{5}\log{(n)}+[\dfrac{2}{5}\log{(p)- 12\log{(p)}]\\\\$

$\underbrace{-24}_{-\frac{120}{5}}\log{(m)+ \dfrac{2}{5}\log{(n)}+\dfrac{-58}{5}\log{(p)}$

$-\dfrac{120}{5}\log{(m)+ \dfrac{2}{5}\log{(n)}+\dfrac{-58}{5}\log{(p)}$

$\dfrac{-120\log{(m)} + 2\log{(n)}-58\log{(p)}}{5}\\\\\mathrm{Aplicamos \: la\: propiedad \:1}\\\\\dfrac{-\log{(m^{120})}+\log{(n^2)}-log{(p^{58})}}{5}\\\\\dfrac{\log{(n^2)}-(\log{(m^{120})}+log{(p^{58})})}{5}\\\\\dfrac{\log{(n^2)}-(\log{(m^{120}p^{58})})}{5}\\\\\dfrac{1}{5}[\log{(n^2)}-\log{(m^{120}p^{58})}]\\\\\mathrm{Aplicamos \: la\: propiedad \:3}\\\\\boxed{\boxed{\boldsymbol{\dfrac{1}{5} \log{(\dfrac{n^2}{m^{120}p^{58}})}}}}$

En el problema 6

$\log_{5}{\left(\dfrac{15ab\sqrt[6]{c}}{3x^2}\right)}\\\\\\\mathrm{Simplificamos\:3}\\\\\\\log_{5}{\left(\dfrac{5ab\sqrt[6]{c}}{x^2}\right)}\\\\\\\mathrm{Aplicamos \: la\: propiedad \:3}\\\\\\\log_{5}{(5ab\sqrt[6]{c})}-\log_{5}{(x^2)}\\\\\\\mathrm{Aplicamos \: la\: propiedad \:2}\$

$[\underbrace{\log_{5}(5)}_{1}+\log_{5}(a)+\log_{5}(b)+\log_{5}{\sqrt[6]{c}}]-\log_{5}{(x^2)}\\\\\boxed{\boxed{\boldsymbol{1+\log_{5}(a)+\log_{5}(b)+\log_{5}{\sqrt[6]{c}}-2\log_{5}{(x)}}}}}$