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

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


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

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

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

Solving
-3ln + 3lnx = -6ln + lnx

Solving for variable 'l'.

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

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

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

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

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

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

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

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