ln(x-5)-ln(x+3)=2

Solution for ln(x-5)-ln(x+3)=2 equation:

Simplifying
ln(x + -5) + -1ln(x + 3) = 2

Reorder the terms:
ln(-5 + x) + -1ln(x + 3) = 2
(-5 * ln + x * ln) + -1ln(x + 3) = 2
(-5ln + lnx) + -1ln(x + 3) = 2

Reorder the terms:
-5ln + lnx + -1ln(3 + x) = 2
-5ln + lnx + (3 * -1ln + x * -1ln) = 2
-5ln + lnx + (-3ln + -1lnx) = 2

Reorder the terms:
-5ln + -3ln + lnx + -1lnx = 2

Combine like terms: -5ln + -3ln = -8ln
-8ln + lnx + -1lnx = 2

Combine like terms: lnx + -1lnx = 0
-8ln + 0 = 2
-8ln = 2

Solving
-8ln = 2

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Divide each side by '-8n'.
l = -0.25n-1

Simplifying
l = -0.25n-1