Solve the logarithmic equation for x. (enter your answers as a comma-separated list. round your answer to four decimal places.) ln (x - 2) + ln (x + 3) = 1

The two logs in ln (x - 2) + ln (x + 3) = 1 can be combined into one:

ln (x - 2) + ln (x + 3) = ln[ (x-2) * (x+3) ] = 1

Then (x-2) (x+3) = e^1 = e

Perform the indicated multiplication.

x^2 + 3x - 2x - 6 = e

1x^2 + 1x - (6+e) = 0

You can use the Quadratic Formula to find the roots here.

Note that a=1, b=1 and c = (6+e).

The discriminant is b^2 - 4ac, or 1^2 - 4 (1) (6+e).

Unfortunately, the discriminant is negative, indicating that you'll have two complex roots.