(i)[2]
By drawing an appropriate pair of graphs, show that the equation $\ln x = 4 - \frac{1}{2}x$ has exactly one real root, $\alpha$.
(ii)[2]
Verify by calculation that the root satisfies $4.5 < \alpha < 5.0$.
(iii)[3]
Apply the iterative formula $x_{n+1} = 8 - 2\ln x_n$ to determine $\alpha$ correct to 2 decimal places, and state every iterate to 4 decimal places.