Question

If ${\log }_{5}a.{\log }_{a}x=2,$ then x is equal to

• A. 125
• B. $a^2$
• C. 25
• D. None of these

Answer 1

Answer: (C)

25

We have,

${\log }_{5}a.{\log }_{a}x=2$

We know that

${\log }_{a}b=\frac{\log b}{\log a}$

Therefore,

$\frac{\log a}{\log 5}\times \frac{\log x}{\log a}=2$

$\frac{\log x}{\log 5}=2$

$\log x=2\log 5$

$\log x=\log 5^2$

$x=25$

Hence, this is the answer.