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

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

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

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

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

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

Multiply (-1 + x) * (1 + x)
5ln + lnx = ln(-1(1 + x) + x(1 + x))
5ln + lnx = ln((1 * -1 + x * -1) + x(1 + x))
5ln + lnx = ln((-1 + -1x) + x(1 + x))
5ln + lnx = ln(-1 + -1x + (1 * x + x * x))
5ln + lnx = ln(-1 + -1x + (1x + x2))

Combine like terms: -1x + 1x = 0
5ln + lnx = ln(-1 + 0 + x2)
5ln + lnx = ln(-1 + x2)
5ln + lnx = (-1 * ln + x2 * ln)
5ln + lnx = (-1ln + lnx2)

Solving
5ln + lnx = -1ln + lnx2

Solving for variable 'l'.

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

Add 'ln' to each side of the equation.
5ln + ln + lnx = -1ln + ln + lnx2

Combine like terms: 5ln + ln = 6ln
6ln + lnx = -1ln + ln + lnx2

Combine like terms: -1ln + ln = 0
6ln + lnx = 0 + lnx2
6ln + lnx = lnx2

Add '-1lnx2' to each side of the equation.
6ln + lnx + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
6ln + lnx + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(6 + x + -1x2) = 0

Factor a trinomial.
ln((3 + -1x)(2 + 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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

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

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

Simplifying
0 = -3 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Add '-1x' to each side of the equation.
x + -1x = -2 + -1x

Combine like terms: x + -1x = 0
0 = -2 + -1x

Simplifying
0 = -2 + -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.