AMC 12 2008b Problem 14

A circle has a radius of $\log_{10}{(a^2)}$ and a circumference of $\log_{10}{(b^4)}$. What is $\log_{a}{b}$?

(Solution)

\textbf{(A)}\ \frac{1}{4\pi} \textbf{(B)}\ \frac{1}{\pi} \textbf{(C)}\ \pi \textbf{(D)}\ 2\pi \textbf{(E)}\ 10^{2\pi}