(i)[2]
By sketching an appropriate pair of graphs, demonstrate that the equation $\ln(x + 2) = 4e^{-x}$ has exactly one real root.
(ii)[2]
Use calculation to show that this root lies between $x = 1$ and $x = 1.5$.
(iii)[3]
Apply the iterative formula $x_{n+1} = \ln\!\left(\dfrac{4}{\ln(x_n + 2)}\right)$ to find the root correct to 2 decimal places. State every iteration result to 4 decimal places.