Ln(x+2)=ln(8-2x)

Solution for Ln(x+2)=ln(8-2x) equation:

Simplifying
Ln(x + 2) = ln(8 + -2x)

Reorder the terms:
nL(2 + x) = ln(8 + -2x)
(2 * nL + x * nL) = ln(8 + -2x)
(2nL + nxL) = ln(8 + -2x)
2nL + nxL = (8 * ln + -2x * ln)
2nL + nxL = (8ln + -2lnx)

Solving
2nL + nxL = 8ln + -2lnx

Solving for variable 'n'.

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

Add '-8ln' to each side of the equation.
2nL + -8ln + nxL = 8ln + -8ln + -2lnx

Reorder the terms:
-8ln + 2nL + nxL = 8ln + -8ln + -2lnx

Combine like terms: 8ln + -8ln = 0
-8ln + 2nL + nxL = 0 + -2lnx
-8ln + 2nL + nxL = -2lnx

Add '2lnx' to each side of the equation.
-8ln + 2nL + 2lnx + nxL = -2lnx + 2lnx

Reorder the terms:
-8ln + 2lnx + 2nL + nxL = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
-8ln + 2lnx + 2nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-8l + 2lx + 2L + 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 '(-8l + 2lx + 2L + xL)' equal to zero and attempt to solve:

Simplifying
-8l + 2lx + 2L + xL = 0

Reorder the terms:
2L + -8l + 2lx + xL = 0

Solving
2L + -8l + 2lx + xL = 0

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

Add '-2L' to each side of the equation.
2L + -8l + 2lx + -2L + xL = 0 + -2L

Reorder the terms:
2L + -2L + -8l + 2lx + xL = 0 + -2L

Combine like terms: 2L + -2L = 0
0 + -8l + 2lx + xL = 0 + -2L
-8l + 2lx + xL = 0 + -2L
Remove the zero:
-8l + 2lx + xL = -2L

Add '8l' to each side of the equation.
-8l + 2lx + 8l + xL = -2L + 8l

Reorder the terms:
-8l + 8l + 2lx + xL = -2L + 8l

Combine like terms: -8l + 8l = 0
0 + 2lx + xL = -2L + 8l
2lx + xL = -2L + 8l

Add '-2lx' to each side of the equation.
2lx + -2lx + xL = -2L + 8l + -2lx

Combine like terms: 2lx + -2lx = 0
0 + xL = -2L + 8l + -2lx
xL = -2L + 8l + -2lx

Add '-1xL' to each side of the equation.
xL + -1xL = -2L + 8l + -2lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -2L + 8l + -2lx + -1xL

Simplifying
0 = -2L + 8l + -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}