ln(x-2)+ln(x-4)=ln(x+2)

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Solution for ln(x-2)+ln(x-4)=ln(x+2) equation:


Simplifying
ln(x + -2) + ln(x + -4) = ln(x + 2)

Reorder the terms:
ln(-2 + x) + ln(x + -4) = ln(x + 2)
(-2 * ln + x * ln) + ln(x + -4) = ln(x + 2)
(-2ln + lnx) + ln(x + -4) = ln(x + 2)

Reorder the terms:
-2ln + lnx + ln(-4 + x) = ln(x + 2)
-2ln + lnx + (-4 * ln + x * ln) = ln(x + 2)
-2ln + lnx + (-4ln + lnx) = ln(x + 2)

Reorder the terms:
-2ln + -4ln + lnx + lnx = ln(x + 2)

Combine like terms: -2ln + -4ln = -6ln
-6ln + lnx + lnx = ln(x + 2)

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

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

Solving
-6ln + 2lnx = 2ln + lnx

Solving for variable 'l'.

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

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

Combine like terms: -6ln + -2ln = -8ln
-8ln + 2lnx = 2ln + -2ln + lnx

Combine like terms: 2ln + -2ln = 0
-8ln + 2lnx = 0 + lnx
-8ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-8ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-8ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-8ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-8 + x) = 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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -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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