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Simplifying 2ln(x2 + -4) = ln(x2 + 8) Reorder the terms: 2ln(-4 + x2) = ln(x2 + 8) (-4 * 2ln + x2 * 2ln) = ln(x2 + 8) (-8ln + 2lnx2) = ln(x2 + 8) Reorder the terms: -8ln + 2lnx2 = ln(8 + x2) -8ln + 2lnx2 = (8 * ln + x2 * ln) -8ln + 2lnx2 = (8ln + lnx2) Solving -8ln + 2lnx2 = 8ln + lnx2 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. -8ln + -8ln + 2lnx2 = 8ln + -8ln + lnx2 Combine like terms: -8ln + -8ln = -16ln -16ln + 2lnx2 = 8ln + -8ln + lnx2 Combine like terms: 8ln + -8ln = 0 -16ln + 2lnx2 = 0 + lnx2 -16ln + 2lnx2 = lnx2 Add '-1lnx2' to each side of the equation. -16ln + 2lnx2 + -1lnx2 = lnx2 + -1lnx2 Combine like terms: 2lnx2 + -1lnx2 = 1lnx2 -16ln + 1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -16ln + 1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-16 + x2) = 0 Factor a difference between two squares. ln((4 + x)(-4 + x)) = 0Subproblem 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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