Question

Qual o resultado dessa questão ?

Answer 1

$\boxed{\log_b{a}=\dfrac{\log{a}}{\log{b}}=\dfrac{\ln{a}}{\ln{b}}}$

$\boxed{\log{a^n}=n\log{a}}$

$x=\log_{32}{4}+(\log_2{8})(\log_{32}{2})\ \therefore\\\\ x=\dfrac{\ln{4}}{\ln{32}}+\bigg(\dfrac{\ln{8}}{\ln{2}}\bigg)\bigg(\dfrac{\ln{2}}{\ln{32}}\bigg)\ \therefore\\\\ x=\dfrac{\ln{2^2}}{\ln{2^5}}+\dfrac{\ln{2^3}}{\ln{2^5}}=\dfrac{2\ln{2}}{5\ln{2}}+\dfrac{3\ln{2}}{5\ln{2}}\ \therefore\\\\\ x=\dfrac{5\ln{2}}{5\ln{2}}\ \therefore\ \boxed{x=1}$