6 It is given that $\int _ { 1 } ^ { a } \ln ( 2 x ) \mathrm { d } x = 1$, where $a > 1$.\\
(i) Show that $a = \frac { 1 } { 2 } \exp \left( 1 + \frac { \ln 2 } { a } \right)$, where $\exp ( x )$ denotes $\mathrm { e } ^ { x }$.\\
(ii) 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.

\hfill \mbox{\textit{CAIE P3 2014 Q6}}