0=ln(x^2-4)

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


Simplifying
0 = ln(x2 + -4)

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

Solving
0 = -4ln + lnx2

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
0 + 4ln = -4ln + 4ln + lnx2
Remove the zero:
4ln = -4ln + 4ln + lnx2

Combine like terms: -4ln + 4ln = 0
4ln = 0 + lnx2
4ln = lnx2

Add '-1lnx2' to each side of the equation.
4ln + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
4ln + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(4 + -1x2) = 0

Factor a difference between two squares.
ln((2 + x)(2 + -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 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x 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 '(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. The solution to this equation could not be determined.

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