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Simplifying ln(x2 + -16) + -1ln(x + 4) = 0 Reorder the terms: ln(-16 + x2) + -1ln(x + 4) = 0 (-16 * ln + x2 * ln) + -1ln(x + 4) = 0 (-16ln + lnx2) + -1ln(x + 4) = 0 Reorder the terms: -16ln + lnx2 + -1ln(4 + x) = 0 -16ln + lnx2 + (4 * -1ln + x * -1ln) = 0 -16ln + lnx2 + (-4ln + -1lnx) = 0 Reorder the terms: -16ln + -4ln + -1lnx + lnx2 = 0 Combine like terms: -16ln + -4ln = -20ln -20ln + -1lnx + lnx2 = 0 Solving -20ln + -1lnx + 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(-20 + -1x + x2) = 0 Factor a trinomial. ln((-4 + -1x)(5 + -1x)) = 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 + -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.Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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