help

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 \(\dfrac{\text{ln}(5)}{\text{ln}(3)} \cdot \dfrac{\text{ln}(9)}{\text{ln}(5)}=\boxed{2}\)

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.