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

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

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

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

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

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

Combine like terms: 2ln + 4ln = 6ln
6ln + lnx + -1lnx = ln(x)

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

Multiply ln * x
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), '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.