Given function

$y = 5^{\log x}$

We need to find its inverse, i.e. express $x$ in terms of $y$.

Take logarithm on both sides

Using logarithm on both sides,

$\log y = \log\left(5^{\log x}\right)$

Now apply the power rule:

$\log y = (\log x)(\log 5)$

Solve for $\log x$

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

Exponentiate to get $x$

$x = 10^{\frac{\log y}{\log 5}}$

Using the identity

$10^{\log a} = a$

we rewrite:

$x = y^{\frac{1}{\log 5}}$

Match with the options

This is exactly:

$x = y^{\frac{1}{\log 5}}$

So the correct option is B.

Quick verification

From

$y = 5^{\log x}$

note that

$5^{\log x} = 10^{(\log 5)(\log x)} = x^{\log 5}$

Hence

$y = x^{\log 5}$

Therefore,

$x = y^{1/\log 5}$

which confirms the result.