3. (a) Given that \(y = \ln x\), find expressions in terms of \(y\) for
- \(\quad \log _ { 2 } x\),
- \(\ln \frac { x ^ { 2 } } { \mathrm { e } }\).
(b) Hence, or otherwise, solve the equation
$$\log _ { 2 } x = 4 - \ln \frac { x ^ { 2 } } { \mathrm { e } } ,$$
giving your answer to 2 decimal places.