6 It is given that \(\int _ { 1 } ^ { a } \ln ( 2 x ) \mathrm { d } x = 1\), where \(a > 1\).
- Show that \(a = \frac { 1 } { 2 } \exp \left( 1 + \frac { \ln 2 } { a } \right)\), where \(\exp ( x )\) denotes \(\mathrm { e } ^ { x }\).
- Use the iterative formula
$$a _ { n + 1 } = \frac { 1 } { 2 } \exp \left( 1 + \frac { \ln 2 } { a _ { n } } \right)$$
to determine the value of \(a\) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.