ln(x+1)+1n(x-1)=1n(8)

Solution for ln(x+1)+1n(x-1)=1n(8) equation:

Simplifying
ln(x + 1) + 1n(x + -1) = 1n(8)

Reorder the terms:
ln(1 + x) + 1n(x + -1) = 1n(8)
(1 * ln + x * ln) + 1n(x + -1) = 1n(8)
(1ln + lnx) + 1n(x + -1) = 1n(8)

Reorder the terms:
1ln + lnx + 1n(-1 + x) = 1n(8)
1ln + lnx + (-1 * 1n + x * 1n) = 1n(8)
1ln + lnx + (-1n + 1nx) = 1n(8)

Reorder the terms for easier multiplication:
1ln + lnx + -1n + 1nx = 1 * 8n

Multiply 1 * 8
1ln + lnx + -1n + 1nx = 8n

Solving
1ln + lnx + -1n + 1nx = 8n

Solving for variable 'l'.

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

Add 'n' to each side of the equation.
1ln + lnx + -1n + n + 1nx = 8n + n

Combine like terms: -1n + n = 0
1ln + lnx + 0 + 1nx = 8n + n
1ln + lnx + 1nx = 8n + n

Combine like terms: 8n + n = 9n
1ln + lnx + 1nx = 9n

Add '-1nx' to each side of the equation.
1ln + lnx + 1nx + -1nx = 9n + -1nx

Combine like terms: 1nx + -1nx = 0
1ln + lnx + 0 = 9n + -1nx
1ln + lnx = 9n + -1nx

Reorder the terms:
1ln + lnx + -9n + nx = 9n + -9n + -1nx + nx

Combine like terms: 9n + -9n = 0
1ln + lnx + -9n + nx = 0 + -1nx + nx
1ln + lnx + -9n + nx = -1nx + nx

Combine like terms: -1nx + nx = 0
1ln + lnx + -9n + nx = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(l + lx + -9 + x) = 0

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

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(l + lx + -9 + x)' equal to zero and attempt to solve:

Simplifying
l + lx + -9 + x = 0

Reorder the terms:
-9 + l + lx + x = 0

Solving
-9 + l + lx + x = 0

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

Add '9' to each side of the equation.
-9 + l + lx + 9 + x = 0 + 9

Reorder the terms:
-9 + 9 + l + lx + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + l + lx + x = 0 + 9
l + lx + x = 0 + 9

Combine like terms: 0 + 9 = 9
l + lx + x = 9

Add '-1x' to each side of the equation.
l + lx + x + -1x = 9 + -1x

Combine like terms: x + -1x = 0
l + lx + 0 = 9 + -1x
l + lx = 9 + -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.