Ln(3x-1)=lnx

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Solution for Ln(3x-1)=lnx equation: 


Simplifying
Ln(3x + -1) = lnx

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

Solving
-1nL + 3nxL = lnx

Solving for variable 'n'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = L + 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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