ln [ (x-3)(x+1) ] = 2ln3 we can write
ln [ ( x - 3) ( x + 1) ] = ln 3^2 forget the natural logs
(x - 3) ( x + 1) = 3^2 simplify
x^2 - 2x - 3 = 9 subtract 9 from both sides
x^2 - 2x - 12 = 0 add 12 to both sides
x^2 - 2x = 12 take (1/2) of 2 = 1....square this = 1...add to both sides
x^2 - 2x + 1 = 13 factor the left side
(x - 1)^2 = 13 take both roots
x - 1 = ±√13 add 1 to both sides
x = ±√13 + 1