Question

Solve:${\log }_{625}125$

Answer 1

Let $a={\log }_{625}125$

$={\log }_{5^4}{5}^3$

We have ${\log }_{a^n}{a}^m=\frac{m}{n}{\log }_{a}a$

$=\frac{3}{4}{\log }_{5}5$ ( since ${\log }_{a}a=1$)

$a=\frac{3}{4}$

${\log }_{625}125=\frac{3}{4}$