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

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

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

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

Reorder the terms for easier multiplication:
-1nL + 3nxL = 2ln + -1lnx + 2ln

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

Combine like terms: 2ln + 2ln = 4ln
-1nL + 3nxL = 4ln + -1lnx

Solving
-1nL + 3nxL = 4ln + -1lnx

Solving for variable 'n'.

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

Add '-4ln' to each side of the equation.
-1nL + -4ln + 3nxL = 4ln + -4ln + -1lnx

Reorder the terms:
-4ln + -1nL + 3nxL = 4ln + -4ln + -1lnx

Combine like terms: 4ln + -4ln = 0
-4ln + -1nL + 3nxL = 0 + -1lnx
-4ln + -1nL + 3nxL = -1lnx

Add 'lnx' to each side of the equation.
-4ln + -1nL + lnx + 3nxL = -1lnx + lnx

Reorder the terms:
-4ln + lnx + -1nL + 3nxL = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-4ln + lnx + -1nL + 3nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-4l + lx + -1L + 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 '(-4l + lx + -1L + 3xL)' equal to zero and attempt to solve:

Simplifying
-4l + lx + -1L + 3xL = 0

Reorder the terms:
-1L + -4l + lx + 3xL = 0

Solving
-1L + -4l + lx + 3xL = 0

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

Add 'L' to each side of the equation.
-1L + -4l + lx + L + 3xL = 0 + L

Reorder the terms:
-1L + L + -4l + lx + 3xL = 0 + L

Combine like terms: -1L + L = 0
0 + -4l + lx + 3xL = 0 + L
-4l + lx + 3xL = 0 + L
Remove the zero:
-4l + lx + 3xL = L

Add '4l' to each side of the equation.
-4l + lx + 4l + 3xL = L + 4l

Reorder the terms:
-4l + 4l + lx + 3xL = L + 4l

Combine like terms: -4l + 4l = 0
0 + lx + 3xL = L + 4l
lx + 3xL = L + 4l

Add '-1lx' to each side of the equation.
lx + -1lx + 3xL = L + 4l + -1lx

Combine like terms: lx + -1lx = 0
0 + 3xL = L + 4l + -1lx
3xL = L + 4l + -1lx

Add '-3xL' to each side of the equation.
3xL + -3xL = L + 4l + -1lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = L + 4l + -1lx + -3xL

Simplifying
0 = L + 4l + -1lx + -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}