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 (logb​a)2017=logb​(a2017)?
Answer Choices:
A. 198
B. 199
C. 398
D. 399
E. 597 Solution:
Let u=logb​a. Because u2017=2017u, either u=0 or u=±20162017​. If u=0, then a=1 and b can be any integer from 2 to 200 . If u=±20162017​, then a=b±20162017​, where again b can be any integer from 2 to 200 . Therefore there are 3⋅199=597​ such ordered pairs.