2004 AMC 12B Problem 3

Attempt Problem 3 of the 2004 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

x

and

y

are positive integers for which

2^x 3^y = 1296,

what is the value of

x + y?

8

9

10

11

12

Factor

1296

into powers of

2

and

3

1296 = 6^4 = 2^4 \cdot 3^4

Factoring,

1296 = 6^4 = 2^4 \cdot 3^4.

Matching exponents gives

x = 4

and

y = 4,

x + y = 8.

Thus, the correct answer is A.

Problem 3 in other years