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

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

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

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

Remove parenthesis around (-3nL + nxL)
-3nL + nxL + -1ln(x + -5) = ln(5)

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

Reorder the terms:
5ln + -1lnx + -3nL + nxL = ln(5)

Reorder the terms for easier multiplication:
5ln + -1lnx + -3nL + nxL = 5ln

Add '-5ln' to each side of the equation.
5ln + -1lnx + -3nL + -5ln + nxL = 5ln + -5ln

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

Combine like terms: 5ln + -5ln = 0
0 + -1lnx + -3nL + nxL = 5ln + -5ln
-1lnx + -3nL + nxL = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-1lnx + -3nL + nxL = 0

Solving
-1lnx + -3nL + nxL = 0

Solving for variable 'l'.

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

Add '3nL' to each side of the equation.
-1lnx + -3nL + 3nL + nxL = 0 + 3nL

Combine like terms: -3nL + 3nL = 0
-1lnx + 0 + nxL = 0 + 3nL
-1lnx + nxL = 0 + 3nL
Remove the zero:
-1lnx + nxL = 3nL

Add '-1nxL' to each side of the equation.
-1lnx + nxL + -1nxL = 3nL + -1nxL

Combine like terms: nxL + -1nxL = 0
-1lnx + 0 = 3nL + -1nxL
-1lnx = 3nL + -1nxL

Divide each side by '-1nx'.
l = -3x-1L + L

Simplifying
l = -3x-1L + L

Reorder the terms:
l = L + -3x-1L