Solve Exponent Problem: 3^x=4^y=12^z

[Bushy]

Given [Math]3^x=4^y =12^z[/Math] show that $$z=\frac{xy}{x+y}$$

I've take logs on both sides and find myself going in circles, any hints?

 

[Greg]

$$3^{xy/(x+y)}=12^{zy/(x+y)}$$

Now try using the fact that $3$ and $4$ are factors of $12$ and that $4^y=3^x$.