ln(x+4)-ln(x-2)=ln(x+5)

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Solution for ln(x+4)-ln(x-2)=ln(x+5) equation: 


Simplifying
ln(x + 4) + -1ln(x + -2) = ln(x + 5)

Reorder the terms:
ln(4 + x) + -1ln(x + -2) = ln(x + 5)
(4 * ln + x * ln) + -1ln(x + -2) = ln(x + 5)
(4ln + lnx) + -1ln(x + -2) = ln(x + 5)

Reorder the terms:
4ln + lnx + -1ln(-2 + x) = ln(x + 5)
4ln + lnx + (-2 * -1ln + x * -1ln) = ln(x + 5)
4ln + lnx + (2ln + -1lnx) = ln(x + 5)

Reorder the terms:
4ln + 2ln + lnx + -1lnx = ln(x + 5)

Combine like terms: 4ln + 2ln = 6ln
6ln + lnx + -1lnx = ln(x + 5)

Combine like terms: lnx + -1lnx = 0
6ln + 0 = ln(x + 5)
6ln = ln(x + 5)

Reorder the terms:
6ln = ln(5 + x)
6ln = (5 * ln + x * ln)
6ln = (5ln + lnx)

Solving
6ln = 5ln + lnx

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
6ln + -5ln = 5ln + -5ln + lnx

Combine like terms: 6ln + -5ln = 1ln
1ln = 5ln + -5ln + lnx

Combine like terms: 5ln + -5ln = 0
1ln = 0 + lnx
1ln = lnx

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + 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.

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