2002 AIME I Problem 6

The solutions to the system of equations

$$\begin{array}{r}\log _{225} x+\log _{64} y=4 \\log _{x} 225-\log _{y} 64=1\end{array}$$

are \left(x_{1}, y_{1}\right) and \left(x_{2}, y_{2}\right). Find \log _{30}\left(x_{1} y_{1} x_{2} y_{2}\right).