Ln(x-3)=ln(2n)

Solution for Ln(x-3)=ln(2n) equation:

Simplifying
Ln(x + -3) = ln(2n)

Reorder the terms:
nL(-3 + x) = ln(2n)
(-3 * nL + x * nL) = ln(2n)
(-3nL + nxL) = ln(2n)

Remove parenthesis around (2n)
-3nL + nxL = ln * 2n

Reorder the terms for easier multiplication:
-3nL + nxL = 2ln * n

Multiply ln * n
-3nL + nxL = 2ln2

Solving
-3nL + nxL = 2ln2

Solving for variable 'n'.

Reorder the terms:
-2ln2 + -3nL + nxL = 2ln2 + -2ln2

Combine like terms: 2ln2 + -2ln2 = 0
-2ln2 + -3nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2ln + -3L + xL) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-2ln + -3L + xL)' equal to zero and attempt to solve:

Simplifying
-2ln + -3L + xL = 0

Reorder the terms:
-3L + -2ln + xL = 0

Solving
-3L + -2ln + xL = 0

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

Add '3L' to each side of the equation.
-3L + -2ln + 3L + xL = 0 + 3L

Reorder the terms:
-3L + 3L + -2ln + xL = 0 + 3L

Combine like terms: -3L + 3L = 0
0 + -2ln + xL = 0 + 3L
-2ln + xL = 0 + 3L
Remove the zero:
-2ln + xL = 3L

Add '-1xL' to each side of the equation.
-2ln + xL + -1xL = 3L + -1xL

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

Divide each side by '-2l'.
n = -1.5l-1L + 0.5l-1xL

Simplifying
n = -1.5l-1L + 0.5l-1xL
Solution
n = {0, -1.5l-1L + 0.5l-1xL}