3.Given that \(x > y > 0\) ,
- by writing \(\log _ { y } x = z\) ,or otherwise,show that \(\log _ { y } x = \frac { 1 } { \log _ { x } y }\) .
- Given also that \(\log _ { x } y = \log _ { y } x\) ,show that \(y = \frac { 1 } { x }\) .
- Solve the simultaneous equations
$$\begin{gathered}
\log _ { x } y = \log _ { y } x \\
\log _ { x } ( x - y ) = \log _ { y } ( x + y )
\end{gathered}$$