- (a) Show that the equation
$$2 \log _ { 2 } y = 5 - \log _ { 2 } x \quad x > 0 , y > 0$$
may be written in the form \(y ^ { 2 } = \frac { k } { x }\) where \(k\) is a constant to be found.
(b) Hence, or otherwise, solve the simultaneous equations
$$\begin{gathered}
2 \log _ { 2 } y = 5 - \log _ { 2 } x
\log _ { x } y = - 3
\end{gathered}$$
for \(x > 0 , y > 0\)