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