ln(x-1)-ln(x+2)=ln(6x-8)

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Solution for ln(x-1)-ln(x+2)=ln(6x-8) equation:


Simplifying
ln(x + -1) + -1ln(x + 2) = ln(6x + -8)

Reorder the terms:
ln(-1 + x) + -1ln(x + 2) = ln(6x + -8)
(-1 * ln + x * ln) + -1ln(x + 2) = ln(6x + -8)
(-1ln + lnx) + -1ln(x + 2) = ln(6x + -8)

Reorder the terms:
-1ln + lnx + -1ln(2 + x) = ln(6x + -8)
-1ln + lnx + (2 * -1ln + x * -1ln) = ln(6x + -8)
-1ln + lnx + (-2ln + -1lnx) = ln(6x + -8)

Reorder the terms:
-1ln + -2ln + lnx + -1lnx = ln(6x + -8)

Combine like terms: -1ln + -2ln = -3ln
-3ln + lnx + -1lnx = ln(6x + -8)

Combine like terms: lnx + -1lnx = 0
-3ln + 0 = ln(6x + -8)
-3ln = ln(6x + -8)

Reorder the terms:
-3ln = ln(-8 + 6x)
-3ln = (-8 * ln + 6x * ln)
-3ln = (-8ln + 6lnx)

Solving
-3ln = -8ln + 6lnx

Solving for variable 'l'.

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

Add '8ln' to each side of the equation.
-3ln + 8ln = -8ln + 8ln + 6lnx

Combine like terms: -3ln + 8ln = 5ln
5ln = -8ln + 8ln + 6lnx

Combine like terms: -8ln + 8ln = 0
5ln = 0 + 6lnx
5ln = 6lnx

Add '-6lnx' to each side of the equation.
5ln + -6lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
5ln + -6lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -6x) = 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 + -6x)' equal to zero and attempt to solve: Simplifying 5 + -6x = 0 Solving 5 + -6x = 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 + -6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x = 0 + -5 -6x = 0 + -5 Combine like terms: 0 + -5 = -5 -6x = -5 Add '6x' to each side of the equation. -6x + 6x = -5 + 6x Combine like terms: -6x + 6x = 0 0 = -5 + 6x Simplifying 0 = -5 + 6x 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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