Problem 3 · 2011 Math Kangaroo
Easy
Algebra & Patterns
substitution
If \(2^{x}=15\) and \(15^{y}=32\), then \(xy\) equals
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Answer: A — 5
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Hint 1 of 2
Rewrite the second equation using the first to get a single power of 2.
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Hint 2 of 2
Replace 15 by 2x, then read the exponent.
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Approach: substitute the first power into the second
- From 2x = 15, the equation 15y = 32 becomes (2x)y = 32.
- That is 2xy = 25, so xy = 5.
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