Question

Como resolvo $Log_{0,25} \sqrt[7]{64}$

Answer 1

$log_{ \frac{1}{4} }(\sqrt[7]{ {2}^{6} }) = x \\ (\frac{1}{4} )^{x} = \sqrt[7]{ {2}^{6} } \\ {2}^{ -2x} = {2}^{ \frac{6}{7} } \\ - 2x = \frac{6}{7} \\ x = - \frac{3}{7}$

Answer 2

Resposta:

$\log _{0,25}\sqrt[7]{64}$ Mudando para a base 2 temos:

$\log _{0,25}\sqrt[7]{64}=\frac{\log_{2}\sqrt[7]{64}}{\log_{2}0,25}$ ⇒

⇒ $\frac{\log_{2}\sqrt[7]{64}}{-2}=\frac{\frac{6}{7}}{2}=-\frac{3}{7}$