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

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

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

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

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

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

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

Combine like terms: lnx + -1lnx = 0
2ln + 0 = 3
2ln = 3

Solving
2ln = 3

Solving for variable 'l'.

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

Divide each side by '2n'.
l = 1.5n-1

Simplifying
l = 1.5n-1