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

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SUMMARY

The discussion focuses on solving the equation 3x = 4y = 12z and demonstrating that z = (xy)/(x+y). Participants suggest using logarithmic properties and the relationship between the bases, specifically that 3 and 4 are factors of 12. The approach involves manipulating the equation to express one variable in terms of the others, ultimately leading to the derived formula.

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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?
 
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$$3^{xy/(x+y)}=12^{zy/(x+y)}$$

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

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