4 The sequence \(x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots\) defined by
$$x _ { 1 } = 1 , \quad x _ { n + 1 } = \frac { x _ { n } } { \ln \left( 2 x _ { n } \right) }$$
converges to the value \(\alpha\).
- Use the iterative formula to find the value of \(\alpha\) correct to 4 significant figures. Give the result of each iteration to 6 significant figures.
- State an equation satisfied by \(\alpha\) and hence determine the exact value of \(\alpha\).