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MAA AMC
AMC 12/AHSME
1966 AMC 12/AHSME
16
More Exponents
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Source:
March 22, 2006
logarithms
Problem Statement
If
4
x
2
x
+
y
=
8
\frac{4^x}{2^{x+y}}=8
2
x
+
y
4
x
=
8
and
9
x
+
y
3
5
y
=
243
\frac{9^{x+y}}{3^{5y}}=243
3
5
y
9
x
+
y
=
243
,
x
x
x
and
y
y
y
are real numbers, then
x
y
xy
x
y
equals:
(A)
12
5
(B)
4
(C)
6
(D)
12
(E)
−
4
\text{(A)} \ \frac{12}{5} \qquad \text{(B)} \ 4 \qquad \text{(C)} \ 6 \qquad \text{(D)} \ 12 \qquad \text{(E)} \ -4
(A)
5
12
(B)
4
(C)
6
(D)
12
(E)
−
4
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