# How do you solve ln(x+1)-ln(x-2)=lnx^2?

Jan 16, 2016

From laws of logs we get

$\ln \left[\frac{x + 1}{x - 2}\right] = \ln {x}^{2}$

$\therefore \frac{x + 1}{x - 2} = {x}^{2}$

$\therefore {x}^{3} - 2 {x}^{2} - x - 1 = 0$

This is now a 3rd degree polynomial so you will have to try using the factor and remainder theorem to find the roots, otherwise you will have to use a numerical technique such as Newton's method of root-finding.

I leave the details as an exercise. Please ask if you are still stuck.