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smc

number theory senior

Problem

If

x

and

y

are positive integers for which

2^{x} 3^{y} = 1296

, what is the value of

x + y

?

(A)

8

(B)

9

(C)

10

(D)

11

Solution

1296 = 2^{4} 3^{4}

and

4 + 4 = 8 ⟹ (A)

.

Final answer

A