Question

If $\left({\log }_{3}a\right)\left({\log }_{a}x\right)=5$, then the value of $x$ is equal to

• A. $3a$
• B. $243$
• C. $15$
• D. $125$

Answer 1

The correct option is B $243$

We have,
$\left({\log }_{3}a\right)\left({\log }_{a}x\right)=5$
By change of base rule, we get
$\left(\frac{\log a}{\log 3}\right)\left(\frac{\log x}{\log a}\right)=5,[\because {\log }_{a}b=\frac{\log a}{\log a}]$
$\Rightarrow \frac{\log x}{\log 3}=5$
$\therefore {\log }_{3}x=5$
$\therefore {x=3}^5=243$