4.
Given that \(\log _ { 2 } x = a\), find, in terms of \(a\), the simplest form of
- \(\quad \log _ { 2 } ( 16 x )\),
- \(\quad \log _ { 2 } \left( \frac { x ^ { 4 } } { 2 } \right)\)
(3) - Hence, or otherwise, solve
$$\log _ { 2 } ( 16 x ) - \log _ { 2 } \left( \frac { x ^ { 4 } } { 2 } \right) = \frac { 1 } { 2 }$$
giving your answer in its simplest surd form.
(Total 9 marks)