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

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

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

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

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

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

Solving for variable 'l'.

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + x) = 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 '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Add '-1x' to each side of the equation.
x + -1x = 3 + -1x

Combine like terms: x + -1x = 0
0 = 3 + -1x

Simplifying
0 = 3 + -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.