(a)[3]
Using sketches of $y = |5 - 2x|$ and $y = 3 \ln x$ on one diagram, show that the equation $|5 - 2x| = 3 \ln x$ has exactly two roots.
(b)[1]
Demonstrate that the larger root has to satisfy $x = 2.5 + 1.5 \ln x$.
(c)[2]
Show, by calculation, that the larger root is between $4.5$ and $5.0$.
(d)[3]
Apply an iterative formula, based on the equation in part (b), to determine the larger root correct to $3$ significant figures. Give each iterate to $5$ significant figures.