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Simplifying ln(x + -2) + ln(x + -3) = ln(12) Reorder the terms: ln(-2 + x) + ln(x + -3) = ln(12) (-2 * ln + x * ln) + ln(x + -3) = ln(12) (-2ln + lnx) + ln(x + -3) = ln(12) Reorder the terms: -2ln + lnx + ln(-3 + x) = ln(12) -2ln + lnx + (-3 * ln + x * ln) = ln(12) -2ln + lnx + (-3ln + lnx) = ln(12) Reorder the terms: -2ln + -3ln + lnx + lnx = ln(12) Combine like terms: -2ln + -3ln = -5ln -5ln + lnx + lnx = ln(12) Combine like terms: lnx + lnx = 2lnx -5ln + 2lnx = ln(12) Reorder the terms for easier multiplication: -5ln + 2lnx = 12ln Solving -5ln + 2lnx = 12ln 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. -5ln + -12ln + 2lnx = 12ln + -12ln Combine like terms: -5ln + -12ln = -17ln -17ln + 2lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -17ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-17 + 2x) = 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 '(-17 + 2x)' equal to zero and attempt to solve: Simplifying -17 + 2x = 0 Solving -17 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 2x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2x = 0 + 17 2x = 0 + 17 Combine like terms: 0 + 17 = 17 2x = 17 Add '-2x' to each side of the equation. 2x + -2x = 17 + -2x Combine like terms: 2x + -2x = 0 0 = 17 + -2x Simplifying 0 = 17 + -2x 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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