Question

Evaluate:

${\log }_5\frac{(25{)}^4}{625}$

Answer 1

We have,

${\log }_5\frac{(25{)}^4}{625}$

$\Rightarrow {\log }_5\frac{(25{)}^4}{(25{)}^2}$

$\Rightarrow {\log }_5(25{)}^2$

$\Rightarrow {\log }_5{5}^4$

$\Rightarrow 4{\log }_{5}5$ $\therefore \log m^n=n\log m$

$\Rightarrow 4\times 1$ $\therefore {\log }_{a}a=1$

$\Rightarrow 4$

Hence, this is the answer.