The solutions to the system of equations \begin{align*} \log_{225}{x}+\log_{64}{y} = 4\\ \log_{x}{225}- \log_{y}{64} = 1 \end{align*} are \((x_1,y_1)\) and \((x_2, y_2)\). Find \(\log_{30}{(x_1y_1x_2y_2)}\).

(第二十届AIME1 2002 第6题)