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

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


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

Remove parenthesis around (3x)
nL * 3x = ln(x + -2)

Reorder the terms for easier multiplication:
3nL * x = ln(x + -2)

Multiply nL * x
3nxL = ln(x + -2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = -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}

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