Ln (x) + Ln (x + 2) = 3
And we can write
Ln [ x ( x + 2) ] = 3
This says that
e^3 = x ( x + 2)
e^3 = x^2 + 2x rearrange
x^2 + 2x - e^3 = 0
Using the quadratic formula, we have that
x = -1 - √ [ 1 + e^3 ] reject this as it makes the logs undefned
or
x = -1 + √ [ 1 + e^3 ] accept