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Simplifying 13lnx2 + -1lnx24 = ln(4x + 12) Reorder the terms: 13lnx2 + -1lnx24 = ln(12 + 4x) 13lnx2 + -1lnx24 = (12 * ln + 4x * ln) 13lnx2 + -1lnx24 = (12ln + 4lnx) Solving 13lnx2 + -1lnx24 = 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. 13lnx2 + -12ln + -1lnx24 = 12ln + -12ln + 4lnx Reorder the terms: -12ln + 13lnx2 + -1lnx24 = 12ln + -12ln + 4lnx Combine like terms: 12ln + -12ln = 0 -12ln + 13lnx2 + -1lnx24 = 0 + 4lnx -12ln + 13lnx2 + -1lnx24 = 4lnx Add '-4lnx' to each side of the equation. -12ln + 13lnx2 + -4lnx + -1lnx24 = 4lnx + -4lnx Reorder the terms: -12ln + -4lnx + 13lnx2 + -1lnx24 = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -12ln + -4lnx + 13lnx2 + -1lnx24 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-12 + -4x + 13x2 + -1x24) = 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 + -4x + 13x2 + -1x24)' equal to zero and attempt to solve: Simplifying -12 + -4x + 13x2 + -1x24 = 0 Solving -12 + -4x + 13x2 + -1x24 = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + -4x + 13x2 + 12 + -1x24 = 0 + 12 Reorder the terms: -12 + 12 + -4x + 13x2 + -1x24 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -4x + 13x2 + -1x24 = 0 + 12 -4x + 13x2 + -1x24 = 0 + 12 Combine like terms: 0 + 12 = 12 -4x + 13x2 + -1x24 = 12 Add '4x' to each side of the equation. -4x + 13x2 + 4x + -1x24 = 12 + 4x Reorder the terms: -4x + 4x + 13x2 + -1x24 = 12 + 4x Combine like terms: -4x + 4x = 0 0 + 13x2 + -1x24 = 12 + 4x 13x2 + -1x24 = 12 + 4x Add '-13x2' to each side of the equation. 13x2 + -13x2 + -1x24 = 12 + 4x + -13x2 Combine like terms: 13x2 + -13x2 = 0 0 + -1x24 = 12 + 4x + -13x2 -1x24 = 12 + 4x + -13x2 Add 'x24' to each side of the equation. -1x24 + x24 = 12 + 4x + -13x2 + x24 Combine like terms: -1x24 + x24 = 0 0 = 12 + 4x + -13x2 + x24 Simplifying 0 = 12 + 4x + -13x2 + x24 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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