Question

If${\log }_5\left({\log }_5\left({\log }_{2}x\right)\right)=0$, then value of $x$ is

• A. $32$
• B. $125$
• C. $625$
• D. $25$

Answer 1

The correct option is A

$32$

Explanation for the correct option

Given that, ${\log }_5\left({\log }_5\left({\log }_{2}x\right)\right)=0$

$\Rightarrow$ ${\log }_5\left({\log }_{2}x\right)=5^0$ $\left[\because {\log }_{a}b=x\Rightarrow b=a^x\right]$

$\Rightarrow$ ${\log }_5\left({\log }_{2}x\right)=1$

$\Rightarrow$ ${\log }_{2}x=5^1$ $\left[\because {\log }_{a}b=x\Rightarrow b=a^x\right]$

$\Rightarrow$ ${\log }_{2}x=5$

$\Rightarrow$ $x=2^5$ $\left[\because {\log }_{a}b=x\Rightarrow b=a^x\right]$

$\Rightarrow$ $x=32$

Hence, option(A) is the correct answer.