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Simplifying lnx2 = ln(12 + -1x) lnx2 = (12 * ln + -1x * ln) lnx2 = (12ln + -1lnx) Solving lnx2 = 12ln + -1lnx 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. -12ln + lnx2 = 12ln + -12ln + -1lnx Combine like terms: 12ln + -12ln = 0 -12ln + lnx2 = 0 + -1lnx -12ln + lnx2 = -1lnx Add 'lnx' to each side of the equation. -12ln + lnx + lnx2 = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -12ln + lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-12 + x + x2) = 0 Factor a trinomial. ln((-4 + -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 '(-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 '(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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