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Simplifying ln(x2) = ln(2) + ln(12 + -1x) Multiply ln * x2 lnx2 = ln(2) + ln(12 + -1x) Reorder the terms for easier multiplication: lnx2 = 2ln + ln(12 + -1x) lnx2 = 2ln + (12 * ln + -1x * ln) lnx2 = 2ln + (12ln + -1lnx) Combine like terms: 2ln + 12ln = 14ln lnx2 = 14ln + -1lnx Solving lnx2 = 14ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. -14ln + lnx2 = 14ln + -14ln + -1lnx Combine like terms: 14ln + -14ln = 0 -14ln + lnx2 = 0 + -1lnx -14ln + lnx2 = -1lnx Add 'lnx' to each side of the equation. -14ln + lnx + lnx2 = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -14ln + lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-14 + x + x2) = 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 '(-14 + x + x2)' equal to zero and attempt to solve: Simplifying -14 + x + x2 = 0 Solving -14 + x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '14' to each side of the equation. -14 + x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + x + x2 = 0 + 14 x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 x + x2 = 14 Add '-1x' to each side of the equation. x + -1x + x2 = 14 + -1x Combine like terms: x + -1x = 0 0 + x2 = 14 + -1x x2 = 14 + -1x Add '-1x2' to each side of the equation. x2 + -1x2 = 14 + -1x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 14 + -1x + -1x2 Simplifying 0 = 14 + -1x + -1x2 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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