ln(x-12)-ln(x-6)=lnx

Solution for ln(x-12)-ln(x-6)=lnx equation:

Simplifying
ln(x + -12) + -1ln(x + -6) = lnx

Reorder the terms:
ln(-12 + x) + -1ln(x + -6) = lnx
(-12 * ln + x * ln) + -1ln(x + -6) = lnx
(-12ln + lnx) + -1ln(x + -6) = lnx

Reorder the terms:
-12ln + lnx + -1ln(-6 + x) = lnx
-12ln + lnx + (-6 * -1ln + x * -1ln) = lnx
-12ln + lnx + (6ln + -1lnx) = lnx

Reorder the terms:
-12ln + 6ln + lnx + -1lnx = lnx

Combine like terms: -12ln + 6ln = -6ln
-6ln + lnx + -1lnx = lnx

Combine like terms: lnx + -1lnx = 0
-6ln + 0 = lnx
-6ln = lnx

Solving
-6ln = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
-6ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-6ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(6 + x) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Add '-1x' to each side of the equation.
x + -1x = -6 + -1x

Combine like terms: x + -1x = 0
0 = -6 + -1x

Simplifying
0 = -6 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.