Resolver \[ \left\{ \begin{array}{l} \log_2 x+\log_4 y+\log_4 z=2 \\ \log_3 y+\log_9 z+\log_9 x=2 \\ \log_4 z+\log_{16} x+\log_{16} y=2 \\ \end{array} \right.\]