ln(3x-2)=ln(6x)

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Solution for ln(3x-2)=ln(6x) equation:


Simplifying
ln(3x + -2) = ln(6x)

Reorder the terms:
ln(-2 + 3x) = ln(6x)
(-2 * ln + 3x * ln) = ln(6x)
(-2ln + 3lnx) = ln(6x)

Remove parenthesis around (6x)
-2ln + 3lnx = ln * 6x

Reorder the terms for easier multiplication:
-2ln + 3lnx = 6ln * x

Multiply ln * x
-2ln + 3lnx = 6lnx

Solving
-2ln + 3lnx = 6lnx

Solving for variable 'l'.

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

Add '-6lnx' to each side of the equation.
-2ln + 3lnx + -6lnx = 6lnx + -6lnx

Combine like terms: 3lnx + -6lnx = -3lnx
-2ln + -3lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-2ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(2 + 3x) = 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 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Add '-3x' to each side of the equation. 3x + -3x = -2 + -3x Combine like terms: 3x + -3x = 0 0 = -2 + -3x Simplifying 0 = -2 + -3x 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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