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2019/20 AHSMC Part 1 Problem 2

Problem 2 of 16

The number of positive integers bb such that log⁡b(64)\log_b(64) is an integer is

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Solution

log⁡b(64)=n\log_b(64) = n means bn=64b^n = 64, so bn=26=43=82=641b^n = 2^6 = 4^3 = 8^2 = 64^1. Thus there are four possible values for bb. The answer is (D).

University of Alberta