Question

Solve ${\log }_5\frac{\sqrt[4]{425}}{625}$

Answer 1

Consider the following question.

${\log }_e\frac{{\left(25\right)}^{\frac{1}{4}}}{625}$

$lo{g}_e\frac{{\left(25\right)}^{\frac{1}{4}}}{625}=lo{g}_e\frac{{\left(5\right)}^{\frac{1}{2}}}{{\left(5\right)}^{\frac{1}{4}}}$

$=\frac{1}{2}{\log }_{e}5-\frac{1}{4}{\log }_{e}5$

$=\frac{1}{4}{\log }_{e}5$

Hence, This is the required answer.