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2017 AMC 12A Problems/Problem 20

Revision as of 15:44, 8 February 2017 by Re1970687 (talk | contribs) (Created page with "==Problem== How many ordered pairs <math>(a,b)</math> such that <math>a</math> is a positive real number and <math>b</math> is an integer between <math>2</math> and <math>200...")
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Problem

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 $(log_b a)^{2017}=log_b(a^{2017})?$

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

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