Equal Logs

Algebra Level 4

$\log_9 p = \log_{12} q = \log_{16} (p + q)$

Suppose that $$p$$ and $$q$$ are positive numbers for which satisfy the equation above.

Then $$q/p$$ can be expressed in the form $$\frac { x + \sqrt{y}}{z}$$, where $$x, y, z$$ are positive integers, and $$y$$ is not divisible by the square of a prime. Find $$x + y + z$$.

×