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

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


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

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

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

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

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

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

Solving for variable 'l'.

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

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

Combine like terms: -2ln + -3ln = -5ln
-5ln + 3lnx = 3ln + -3ln + -1lnx

Combine like terms: 3ln + -3ln = 0
-5ln + 3lnx = 0 + -1lnx
-5ln + 3lnx = -1lnx

Add 'lnx' to each side of the equation.
-5ln + 3lnx + lnx = -1lnx + lnx

Combine like terms: 3lnx + lnx = 4lnx
-5ln + 4lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-5ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + 4x) = 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 '(-5 + 4x)' equal to zero and attempt to solve: Simplifying -5 + 4x = 0 Solving -5 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4x = 0 + 5 4x = 0 + 5 Combine like terms: 0 + 5 = 5 4x = 5 Add '-4x' to each side of the equation. 4x + -4x = 5 + -4x Combine like terms: 4x + -4x = 0 0 = 5 + -4x Simplifying 0 = 5 + -4x 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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