AMC 12 2010a Problem 11

The solution of the equation $7^{x+7} = 8^x$ can be expressed in the form $x = \log_b 7^7$. What is $b$?

\textbf{(A)}\ \frac{7}{15} \textbf{(B)}\ \frac{7}{8} \textbf{(C)}\ \frac{8}{7} \textbf{(D)}\ \frac{15}{8} \textbf{(E)}\ \frac{15}{7}