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

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


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

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

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

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

Solving for variable 'l'.

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

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

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

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

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

Simplifying
0 = 1 + -2x

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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