4. (a) Given that \(y = \log _ { 2 } x\), find expressions in terms of \(y\) for
- \(\quad \log _ { 2 } \left( \frac { x } { 2 } \right)\),
- \(\quad \log _ { 2 } ( \sqrt { x } )\).
(b) Hence, or otherwise, solve the equation
$$2 \log _ { 2 } \left( \frac { x } { 2 } \right) + \log _ { 2 } ( \sqrt { x } ) = 8$$