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

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

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

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

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

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

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 + 3nxL = 2ln + -2ln + lnx

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2l + -1lx + -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 '(-2l + -1lx + -1L + 3xL)' equal to zero and attempt to solve:

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

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

Solving
-1L + -2l + -1lx + 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 + -2l + -1lx + L + 3xL = 0 + L

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

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

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

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

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

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

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

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

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

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