ln(x+1)-ln(x+-1)=ln(x+5)

Solution for ln(x+1)-ln(x+-1)=ln(x+5) equation:

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

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

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

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

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

Combine like terms: lnx + -1lnx = 0
2ln + 0 = ln(x + 5)
2ln = ln(x + 5)

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

Solving
2ln = 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.
2ln + -5ln = 5ln + -5ln + lnx

Combine like terms: 2ln + -5ln = -3ln
-3ln = 5ln + -5ln + lnx

Combine like terms: 5ln + -5ln = 0
-3ln = 0 + lnx
-3ln = lnx

Add '-1lnx' to each side of the equation.
-3ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-3ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Add '-1x' to each side of the equation.
x + -1x = -3 + -1x

Combine like terms: x + -1x = 0
0 = -3 + -1x

Simplifying
0 = -3 + -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.