Question

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

Answer 1

From laws of logs we get

`ln[(x+1)/(x-2)]=lnx^2`

`therefore (x+1)/(x-2)=x^2`

`therefore x^3-2x^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.