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2004 AMC 12B Problems/Problem 3

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Problem

If x and y are positive integers for which 2^x3^y=1296, what is the value of x+y?

(\mathrm {A})\ 8 \qquad (\mathrm {B})\ 9 \qquad (\mathrm {C})\ 10 \qquad (\mathrm {D})\ 11 \qquad (\mathrm {E})\ 12

Solution

1296 = 2^4 3^4 and 4+4=\boxed{8} \Longrightarrow \mathrm{(A)}.

See Also

2004 AMC 12B (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
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