AMC 12 2017a Problem 20

How many ordered pairs $(a,b)$ such that $a$ is a positive real number and $b$ is an integer between $2$ and $200$, inclusive, satisfy the equation $(\log_b a)^{2017}=\log_b(a^{2017})?$

\textbf{(A)}\ 198 \textbf{(B)}\ 199 \textbf{(C)}\ 398 \textbf{(D)}\ 399 \textbf{(E)}\ 597