Ln(3x+1)=ln(2x-8)

Solution for Ln(3x+1)=ln(2x-8) equation:

Simplifying
Ln(3x + 1) = ln(2x + -8)

Reorder the terms:
nL(1 + 3x) = ln(2x + -8)
(1 * nL + 3x * nL) = ln(2x + -8)
(1nL + 3nxL) = ln(2x + -8)

Reorder the terms:
1nL + 3nxL = ln(-8 + 2x)
1nL + 3nxL = (-8 * ln + 2x * ln)
1nL + 3nxL = (-8ln + 2lnx)

Solving
1nL + 3nxL = -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.
1nL + 8ln + 3nxL = -8ln + 8ln + 2lnx

Reorder the terms:
8ln + 1nL + 3nxL = -8ln + 8ln + 2lnx

Combine like terms: -8ln + 8ln = 0
8ln + 1nL + 3nxL = 0 + 2lnx
8ln + 1nL + 3nxL = 2lnx

Add '-2lnx' to each side of the equation.
8ln + 1nL + -2lnx + 3nxL = 2lnx + -2lnx

Reorder the terms:
8ln + -2lnx + 1nL + 3nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
8ln + -2lnx + 1nL + 3nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(8l + -2lx + L + 3xL) = 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 + L + 3xL)' equal to zero and attempt to solve:

Simplifying
8l + -2lx + L + 3xL = 0

Reorder the terms:
L + 8l + -2lx + 3xL = 0

Solving
L + 8l + -2lx + 3xL = 0

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

Add '-1L' to each side of the equation.
L + 8l + -2lx + -1L + 3xL = 0 + -1L

Reorder the terms:
L + -1L + 8l + -2lx + 3xL = 0 + -1L

Combine like terms: L + -1L = 0
0 + 8l + -2lx + 3xL = 0 + -1L
8l + -2lx + 3xL = 0 + -1L
Remove the zero:
8l + -2lx + 3xL = -1L

Add '-8l' to each side of the equation.
8l + -2lx + -8l + 3xL = -1L + -8l

Reorder the terms:
8l + -8l + -2lx + 3xL = -1L + -8l

Combine like terms: 8l + -8l = 0
0 + -2lx + 3xL = -1L + -8l
-2lx + 3xL = -1L + -8l

Add '2lx' to each side of the equation.
-2lx + 2lx + 3xL = -1L + -8l + 2lx

Combine like terms: -2lx + 2lx = 0
0 + 3xL = -1L + -8l + 2lx
3xL = -1L + -8l + 2lx

Add '-3xL' to each side of the equation.
3xL + -3xL = -1L + -8l + 2lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = -1L + -8l + 2lx + -3xL

Simplifying
0 = -1L + -8l + 2lx + -3xL

The solution to this equation could not be determined.

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