(a)[3]
If $2\ln(x+1)+\ln x=\ln(x+9)$, prove that $x=\sqrt{\frac{9}{x+2}}$.
(b)[2]
The equation $x=\sqrt{\frac{9}{x+2}}$ is known to have one root. By calculation, show that this root is located between $1.5$ and $2.0$.
(c)[3]
Use an iteration method, based on the equation in part (b), to determine the root correct to $3$ significant figures. Write each iteration to $5$ significant figures.