Show that for any positive numbers $\displaystyle x$ and $\displaystyle a$ (with $\displaystyle x$ not equal to $\displaystyle 1$) $\displaystyle \log_{x^2} a = \frac{1}{2} \log_{x} a $.

Also, generalize the assertion in the problem above to powers other than $\displaystyle x^2 $.

Thank you (: