ln(x^2-4)-2ln(x+2)=0

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Solution for ln(x^2-4)-2ln(x+2)=0 equation:


Simplifying
ln(x2 + -4) + -2ln(x + 2) = 0

Reorder the terms:
ln(-4 + x2) + -2ln(x + 2) = 0
(-4 * ln + x2 * ln) + -2ln(x + 2) = 0
(-4ln + lnx2) + -2ln(x + 2) = 0

Reorder the terms:
-4ln + lnx2 + -2ln(2 + x) = 0
-4ln + lnx2 + (2 * -2ln + x * -2ln) = 0
-4ln + lnx2 + (-4ln + -2lnx) = 0

Reorder the terms:
-4ln + -4ln + -2lnx + lnx2 = 0

Combine like terms: -4ln + -4ln = -8ln
-8ln + -2lnx + lnx2 = 0

Solving
-8ln + -2lnx + lnx2 = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-8 + -2x + x2) = 0

Factor a trinomial.
ln((-2 + -1x)(4 + -1x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Add 'x' to each side of the equation. -1x + x = 2 + x Combine like terms: -1x + x = 0 0 = 2 + x Simplifying 0 = 2 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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