ln(2x)-ln(3x-1)=0

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Solution for ln(2x)-ln(3x-1)=0 equation: 


Simplifying
ln(2x) + -1ln(3x + -1) = 0

Remove parenthesis around (2x)
ln * 2x + -1ln(3x + -1) = 0

Reorder the terms for easier multiplication:
2ln * x + -1ln(3x + -1) = 0

Multiply ln * x
2lnx + -1ln(3x + -1) = 0

Reorder the terms:
2lnx + -1ln(-1 + 3x) = 0
2lnx + (-1 * -1ln + 3x * -1ln) = 0
2lnx + (1ln + -3lnx) = 0

Reorder the terms:
1ln + 2lnx + -3lnx = 0

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

Solving
1ln + -1lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + -1x) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Add 'x' to each side of the equation.
-1x + x = -1 + x

Combine like terms: -1x + x = 0
0 = -1 + x

Simplifying
0 = -1 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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