Question

questão do iezzi sobre log

Answer 1

$\mathsf{y=log \sqrt[3]{4}^{ \sqrt{2}}+log \sqrt[3]{100}^{ \sqrt[6]{0,1}}-log100 }$

Vamos resolver primeiro:

$log \sqrt[3]{4}^{ \sqrt{2}}=x \\ \\ \sqrt{2} = ( \sqrt[3]{4})^x \\ \\ 2^{ \frac{1}{2}}=( \sqrt[3]{2^2})^x \\ \\ 2^ \frac{1}{2} = 2^{ \frac{2x}{3}} \\ \\ \frac{1}{2}= \frac{2x}{3} \\ \\ 4x=3 \\ \\ \boxed{x= \frac{3}{4}}$

Agora:

$log \sqrt[3]{100}^ \sqrt[6]{0,1} }=x \\ \\ \sqrt[6]{ \frac{1}{10}}= (\sqrt[3]{10^2} )^x \\ \\ \sqrt[6]{10^-^1} = 10^{ \frac{2x}{3} } \\ \\ 10^{ \frac{-1}{6} }=10^{ \frac{2x}{3} } \\ \\ \frac{-1}{6} = \frac{2x}{3} \\ \\ 12x=-3 \\ \\ x= \frac{-3}{12} =\boxed{ \frac{-1}{4}}$

O log de 100 é 2, pois tem dois zeros.

$log100=\boxed{2}$

$y = \frac{3}{4} - \frac{1}{4} - 2= \frac{3-1-8}{4} = \frac{-6}{4} = \boxed{ \frac{-3}{2} }$