Question

Solve:

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

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is C $6$

We have,

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

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

$\Rightarrow {\log }_5(25{)}^3$

$\Rightarrow {\log }_5{5}^6$

$\Rightarrow 6{\log }_{5}5$ $\therefore \log m^n=n\log m$

$\Rightarrow 6\times 1$ $\therefore {\log }_{a}a=1$

$\Rightarrow 6$

Hence, this is the answer.