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

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


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

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

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

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

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

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

Solving
-2ln + -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), '-1ln'.
-1ln(2 + x) = 0

Ignore the factor -1.

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Add '-1x' to each side of the equation.
x + -1x = -2 + -1x

Combine like terms: x + -1x = 0
0 = -2 + -1x

Simplifying
0 = -2 + -1x

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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