Question

Dados log2=0,301e log3=0,477, calcule log raiz cubica de a ao quadrado vezes b.

Answer 1

Oi,

use as propriedades de log:

$log(ab)~\to~log(a*b)\to~loga+logb\\ logb^k~\to~k*logb$

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$log \sqrt[3]{a^2b}=log \sqrt[3]{a^2*b^1} \\\\ log \sqrt[3]{a^2b}= log(a^{ \tfrac{2}{3} }*b^{ \tfrac{1}{3} })\\\\ log \sqrt[3]{a^2b}=loga^{ \tfrac{2}{3} }+logb^{ \tfrac{1}{3} }\\\\ log \sqrt[3]{a^2b}= \dfrac{2}{3}*loga+ \dfrac{1}{3}*logb\\\\ log \sqrt[3]{a^2b}= \dfrac{2}{3}*0,301+ \dfrac{1}{3}*0,477\\\\ log \sqrt[3]{a^2b}=0,2+0,159\\\\ \boxed{log \sqrt[3]{a^2b}\approx0,359}$

Espero ter ajudado e tenha ótimos estudos =))