ln(4x-6)=ln(6x+12)

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Solution for ln(4x-6)=ln(6x+12) equation:


Simplifying
ln(4x + -6) = ln(6x + 12)

Reorder the terms:
ln(-6 + 4x) = ln(6x + 12)
(-6 * ln + 4x * ln) = ln(6x + 12)
(-6ln + 4lnx) = ln(6x + 12)

Reorder the terms:
-6ln + 4lnx = ln(12 + 6x)
-6ln + 4lnx = (12 * ln + 6x * ln)
-6ln + 4lnx = (12ln + 6lnx)

Solving
-6ln + 4lnx = 12ln + 6lnx

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
-6ln + -12ln + 4lnx = 12ln + -12ln + 6lnx

Combine like terms: -6ln + -12ln = -18ln
-18ln + 4lnx = 12ln + -12ln + 6lnx

Combine like terms: 12ln + -12ln = 0
-18ln + 4lnx = 0 + 6lnx
-18ln + 4lnx = 6lnx

Add '-6lnx' to each side of the equation.
-18ln + 4lnx + -6lnx = 6lnx + -6lnx

Combine like terms: 4lnx + -6lnx = -2lnx
-18ln + -2lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-18ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), '-2ln'.
-2ln(9 + x) = 0

Ignore the factor -2.

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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -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.

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