ln(6+x)=ln(x-6)-ln(x-4)

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Solution for ln(6+x)=ln(x-6)-ln(x-4) equation: 


Simplifying
ln(6 + x) = ln(x + -6) + -1ln(x + -4)
(6 * ln + x * ln) = ln(x + -6) + -1ln(x + -4)
(6ln + lnx) = ln(x + -6) + -1ln(x + -4)

Reorder the terms:
6ln + lnx = ln(-6 + x) + -1ln(x + -4)
6ln + lnx = (-6 * ln + x * ln) + -1ln(x + -4)
6ln + lnx = (-6ln + lnx) + -1ln(x + -4)

Reorder the terms:
6ln + lnx = -6ln + lnx + -1ln(-4 + x)
6ln + lnx = -6ln + lnx + (-4 * -1ln + x * -1ln)
6ln + lnx = -6ln + lnx + (4ln + -1lnx)

Reorder the terms:
6ln + lnx = -6ln + 4ln + lnx + -1lnx

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

Combine like terms: lnx + -1lnx = 0
6ln + lnx = -2ln + 0
6ln + lnx = -2ln

Solving
6ln + lnx = -2ln

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.
6ln + 2ln + lnx = -2ln + 2ln

Combine like terms: 6ln + 2ln = 8ln
8ln + lnx = -2ln + 2ln

Combine like terms: -2ln + 2ln = 0
8ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(8 + x) = 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 '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Add '-1x' to each side of the equation.
x + -1x = -8 + -1x

Combine like terms: x + -1x = 0
0 = -8 + -1x

Simplifying
0 = -8 + -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.

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