The inverse of $$y = 5^{\log x}$$ is:

We need the inverse function of $$y = 5^{\log x}$$.

Taking logarithm (base 10) on both sides: $$\log y = \log x \cdot \log 5$$.

Solving for $$\log x$$: $$\log x = \frac{\log y}{\log 5}$$.

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

We can write this as $$x = \left(10^{\log y}\right)^{1/\log 5} = y^{1/\log 5}$$, since $$10^{\log y} = y$$.

For the inverse function, we swap $$x$$ and $$y$$: $$y = x^{1/\log 5}$$.

This matches Option C: $$y = x^{\frac{1}{\log 5}}$$.