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.