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help

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If 3^x = 5 and 5^y = 9, then find xy.

Jun 12, 2020

#1
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i'm pretty sure there's a much better way to do this but here's my solution:

$$3^x=5 \text{ is equal to } \dfrac{\text{ln}(5)}{\text{ln}(3)}$$

$$5^y=9 \text{ is equal to } \dfrac{\text{ln}(9)}{\text{ln}(5)}$$

so, $$xy$$ is equal to $$\dfrac{\text{ln}(5)}{\text{ln}(3)} \cdot \dfrac{\text{ln}(9)}{\text{ln}(5)}=\boxed{2}$$

Jun 12, 2020
#2
+17
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Here's another solution:

3^x = 5 can be written as log3(5) = x and 5^y = 9 can be written as 2*log5(3) = y. Thus, xy is just log3(5)*2*log5(3) = 2*1 = 2.

Jun 12, 2020