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2004 AMC 12B Problem 3

Problem 3 of 25EasierNumber TheoryArithmetic

If xx and yy are positive integers for which 2x3y=1296,2^x 3^y = 1296, what is the value of x+y?x + y?

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Solution

Factoring, 1296=64=24⋅34.1296 = 6^4 = 2^4 \cdot 3^4. Matching exponents gives x=4x = 4 and y=4,y = 4, so x+y=8.x + y = 8. Thus, the correct answer is A.
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Tagged: prime factorization · exponent

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