2017 AMC 12A 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\qquad\textbf{(B)}\ 199\qquad\textbf{(C)}\ 398\qquad\textbf{(D)}\ 399\qquad\textbf{(E)}\ 597

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.