Ln(x+1)=2ln(x-1)

Solution for Ln(x+1)=2ln(x-1) equation:

Simplifying
Ln(x + 1) = 2ln(x + -1)

Reorder the terms:
nL(1 + x) = 2ln(x + -1)
(1 * nL + x * nL) = 2ln(x + -1)
(1nL + nxL) = 2ln(x + -1)

Reorder the terms:
1nL + nxL = 2ln(-1 + x)
1nL + nxL = (-1 * 2ln + x * 2ln)
1nL + nxL = (-2ln + 2lnx)

Solving
1nL + nxL = -2ln + 2lnx

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.
1nL + 2ln + nxL = -2ln + 2ln + 2lnx

Reorder the terms:
2ln + 1nL + nxL = -2ln + 2ln + 2lnx

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

Add '-2lnx' to each side of the equation.
2ln + 1nL + -2lnx + nxL = 2lnx + -2lnx

Reorder the terms:
2ln + -2lnx + 1nL + nxL = 2lnx + -2lnx

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(2l + -2lx + L + 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 + -2lx + L + xL)' equal to zero and attempt to solve:

Simplifying
2l + -2lx + L + xL = 0

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

Solving
L + 2l + -2lx + xL = 0

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

Add '-1L' to each side of the equation.
L + 2l + -2lx + -1L + xL = 0 + -1L

Reorder the terms:
L + -1L + 2l + -2lx + xL = 0 + -1L

Combine like terms: L + -1L = 0
0 + 2l + -2lx + xL = 0 + -1L
2l + -2lx + xL = 0 + -1L
Remove the zero:
2l + -2lx + xL = -1L

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

Reorder the terms:
2l + -2l + -2lx + xL = -1L + -2l

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

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

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

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

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

Simplifying
0 = -1L + -2l + 2lx + -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}