Question

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

Answer 1

`x=3.30`

Explanation:

`In(x+1)-In(x-2)=Inx`
`In(x+1)/(x-2)=Inx`
`(x+1)/(x-2)=x`
`x+1=x(x-2)`
`x+1=x^2-2x`
`x^2-3x-1=0`

Using quadratic formula,
`x=(3+-sqrt(9+4))/2`
`x=(3+sqrt13)/2 or (3-sqrt13)/2`
`x=3.30 or -0.302`

BUT you can't log a NEGATIVE number so `x=-0.302`

Therefore, `x=3.30` is the only answer