Question

Quanto é log de 128 na raiz quinta de 2?

Answer 1

$log 128_{ \sqrt[5]{2} }= log 2^{7} _{ \sqrt[5]{2} }= log 2^{7} _{ 2^{ \frac{1}{5} } }=7log 2_{ 2^{ \frac{1}{5} } }= \frac{7}{ \frac{1}{5} } log 2_{2} = \frac{7}{1}* \frac{5}{1}*1=35 \\ propriedade:log a_{a}=1$

Answer 2

$\log_{\sqrt[5]{2}}128=\\\\\\\frac{\log_{10}128}{\log_{10}\sqrt[5]{2}}=\\\\\\\frac{\log2^7}{\log2^{\frac{1}{5}}}=\\\\\\\frac{7\cdot\log2}{\frac{1}{5}\cdot\log2}=\\\\\\7\div\frac{1}{5}=\\\\\\7\times\frac{5}{1}=\\\\\boxed{35}$