AMC12 2004 B
AMC12 2004 B · Q3
AMC12 2004 B · Q3. It mainly tests Primes & prime factorization.
If $x$ and $y$ are positive integers for which $2^x3^y=1296$, what is the value of $x+y$?
如果 $x$ 和 $y$ 是正整数，使得 $2^x3^y=1296$，那么 $x+y$ 的值是多少？
(A)
8
8
(B)
9
9
(C)
10
10
(D)
11
11
(E)
12
12
Answer
Correct choice: (A)
正确答案：（A）
Solution
$1296 = 2^4 3^4$ and $4+4=\boxed{8} \Longrightarrow \mathrm{(A)}$.
$1296 = 2^4 3^4$，因此 $4+4=\boxed{8} \Longrightarrow \mathrm{(A)}$。
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