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Simplifying ln(x2 + -9) = ln(12 + -4x) Reorder the terms: ln(-9 + x2) = ln(12 + -4x) (-9 * ln + x2 * ln) = ln(12 + -4x) (-9ln + lnx2) = ln(12 + -4x) -9ln + lnx2 = (12 * ln + -4x * ln) -9ln + lnx2 = (12ln + -4lnx) Solving -9ln + lnx2 = 12ln + -4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. -9ln + -12ln + lnx2 = 12ln + -12ln + -4lnx Combine like terms: -9ln + -12ln = -21ln -21ln + lnx2 = 12ln + -12ln + -4lnx Combine like terms: 12ln + -12ln = 0 -21ln + lnx2 = 0 + -4lnx -21ln + lnx2 = -4lnx Add '4lnx' to each side of the equation. -21ln + 4lnx + lnx2 = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 -21ln + 4lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-21 + 4x + x2) = 0 Factor a trinomial. ln((-7 + -1x)(3 + -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 '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Add 'x' to each side of the equation. -1x + x = 7 + x Combine like terms: -1x + x = 0 0 = 7 + x Simplifying 0 = 7 + 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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