ln(x+4)-ln(x)=ln(x-2)

Solution for ln(x+4)-ln(x)=ln(x-2) equation:

Simplifying
ln(x + 4) + -1ln(x) = ln(x + -2)

Reorder the terms:
ln(4 + x) + -1ln(x) = ln(x + -2)
(4 * ln + x * ln) + -1ln(x) = ln(x + -2)
(4ln + lnx) + -1ln(x) = ln(x + -2)

Multiply ln * x
4ln + lnx + -1lnx = ln(x + -2)

Combine like terms: lnx + -1lnx = 0
4ln + 0 = ln(x + -2)
4ln = ln(x + -2)

Reorder the terms:
4ln = ln(-2 + x)
4ln = (-2 * ln + x * ln)
4ln = (-2ln + lnx)

Solving
4ln = -2ln + lnx

Solving for variable 'l'.

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

Add '2ln' to each side of the equation.
4ln + 2ln = -2ln + 2ln + lnx

Combine like terms: 4ln + 2ln = 6ln
6ln = -2ln + 2ln + lnx

Combine like terms: -2ln + 2ln = 0
6ln = 0 + lnx
6ln = lnx

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), 'ln'.
ln(6 + -1x) = 0

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 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

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

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

Simplifying
0 = -6 + x

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.