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

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

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

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

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

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

Reorder the terms:
5nL + nxL = -1ln + -1ln + lnx + -1lnx

Combine like terms: -1ln + -1ln = -2ln
5nL + nxL = -2ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
5nL + nxL = -2ln + 0
5nL + nxL = -2ln

Solving
5nL + nxL = -2ln

Solving for variable 'n'.

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

Add '2ln' to each side of the equation.
5nL + 2ln + nxL = -2ln + 2ln

Reorder the terms:
2ln + 5nL + nxL = -2ln + 2ln

Combine like terms: -2ln + 2ln = 0
2ln + 5nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(2l + 5L + xL) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(2l + 5L + xL)' equal to zero and attempt to solve:

Simplifying
2l + 5L + xL = 0

Reorder the terms:
5L + 2l + xL = 0

Solving
5L + 2l + xL = 0

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

Add '-5L' to each side of the equation.
5L + 2l + -5L + xL = 0 + -5L

Reorder the terms:
5L + -5L + 2l + xL = 0 + -5L

Combine like terms: 5L + -5L = 0
0 + 2l + xL = 0 + -5L
2l + xL = 0 + -5L
Remove the zero:
2l + xL = -5L

Add '-2l' to each side of the equation.
2l + -2l + xL = -5L + -2l

Combine like terms: 2l + -2l = 0
0 + xL = -5L + -2l
xL = -5L + -2l

Add '-1xL' to each side of the equation.
xL + -1xL = -5L + -2l + -1xL

Combine like terms: xL + -1xL = 0
0 = -5L + -2l + -1xL

Simplifying
0 = -5L + -2l + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}