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Simplifying ln(x2 + -144) + -1ln(x + 12) = 0 Reorder the terms: ln(-144 + x2) + -1ln(x + 12) = 0 (-144 * ln + x2 * ln) + -1ln(x + 12) = 0 (-144ln + lnx2) + -1ln(x + 12) = 0 Reorder the terms: -144ln + lnx2 + -1ln(12 + x) = 0 -144ln + lnx2 + (12 * -1ln + x * -1ln) = 0 -144ln + lnx2 + (-12ln + -1lnx) = 0 Reorder the terms: -144ln + -12ln + -1lnx + lnx2 = 0 Combine like terms: -144ln + -12ln = -156ln -156ln + -1lnx + lnx2 = 0 Solving -156ln + -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(-156 + -1x + x2) = 0 Factor a trinomial. ln((-12 + -1x)(13 + -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 '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Add 'x' to each side of the equation. -1x + x = 12 + x Combine like terms: -1x + x = 0 0 = 12 + x Simplifying 0 = 12 + 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 '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Add 'x' to each side of the equation. -1x + x = -13 + x Combine like terms: -1x + x = 0 0 = -13 + x Simplifying 0 = -13 + 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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