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2015/16 AHSMC Part 1 Problem 2

Problem 2 of 16

Let mm, nn be positive integers such that 230330=8m9n2^{30}3^{30} = 8^m 9^n. Determine the value of m+nm + n.

Answer choices

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Solution

The equation can be written as 230−3m=32n−302^{30-3m} = 3^{2n-30}, hence m=10m = 10, n=15n = 15, thus m+n=25m + n = 25. The answer is (C).

University of Alberta