By sketching the graphs of
$$y = | 5 - 2 x | \quad \text { and } \quad y = 3 \ln x$$
on the same diagram, show that the equation \(| 5 - 2 x | = 3 \ln x\) has exactly two roots.
Show that the value of the larger root satisfies the equation \(x = 2.5 + 1.5 \ln x\).
Show by calculation that the value of the larger root lies between 4.5 and 5.0.
Use an iterative formula, based on the equation in part (b), to find the value of the larger root correct to 3 significant figures. Give the result of each iteration to 5 significant figures.