Ln(x+5)=ln(12x)

Solution for Ln(x+5)=ln(12x) equation:

Simplifying
Ln(x + 5) = ln(12x)

Reorder the terms:
nL(5 + x) = ln(12x)
(5 * nL + x * nL) = ln(12x)
(5nL + nxL) = ln(12x)

Remove parenthesis around (12x)
5nL + nxL = ln * 12x

Reorder the terms for easier multiplication:
5nL + nxL = 12ln * x

Multiply ln * x
5nL + nxL = 12lnx

Solving
5nL + nxL = 12lnx

Solving for variable 'n'.

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

Add '-12lnx' to each side of the equation.
5nL + -12lnx + nxL = 12lnx + -12lnx

Reorder the terms:
-12lnx + 5nL + nxL = 12lnx + -12lnx

Combine like terms: 12lnx + -12lnx = 0
-12lnx + 5nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-12lx + 5L + 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 '(-12lx + 5L + xL)' equal to zero and attempt to solve:

Simplifying
-12lx + 5L + xL = 0

Reorder the terms:
5L + -12lx + xL = 0

Solving
5L + -12lx + xL = 0

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

Add '-5L' to each side of the equation.
5L + -12lx + -5L + xL = 0 + -5L

Reorder the terms:
5L + -5L + -12lx + xL = 0 + -5L

Combine like terms: 5L + -5L = 0
0 + -12lx + xL = 0 + -5L
-12lx + xL = 0 + -5L
Remove the zero:
-12lx + xL = -5L

Add '12lx' to each side of the equation.
-12lx + 12lx + xL = -5L + 12lx

Combine like terms: -12lx + 12lx = 0
0 + xL = -5L + 12lx
xL = -5L + 12lx

Add '-1xL' to each side of the equation.
xL + -1xL = -5L + 12lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -5L + 12lx + -1xL

Simplifying
0 = -5L + 12lx + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}