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

 Jun 12, 2020
 #1
avatar+732 
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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
avatar+17 
+1

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. smiley

 Jun 12, 2020

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