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Simplifying ln(12 + -1x) = lnx + ln(x + -5) (12 * ln + -1x * ln) = lnx + ln(x + -5) (12ln + -1lnx) = lnx + ln(x + -5) Reorder the terms: 12ln + -1lnx = lnx + ln(-5 + x) 12ln + -1lnx = lnx + (-5 * ln + x * ln) 12ln + -1lnx = lnx + (-5ln + lnx) Reorder the terms: 12ln + -1lnx = -5ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx 12ln + -1lnx = -5ln + 2lnx Solving 12ln + -1lnx = -5ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 12ln + 5ln + -1lnx = -5ln + 5ln + 2lnx Combine like terms: 12ln + 5ln = 17ln 17ln + -1lnx = -5ln + 5ln + 2lnx Combine like terms: -5ln + 5ln = 0 17ln + -1lnx = 0 + 2lnx 17ln + -1lnx = 2lnx Add '-2lnx' to each side of the equation. 17ln + -1lnx + -2lnx = 2lnx + -2lnx Combine like terms: -1lnx + -2lnx = -3lnx 17ln + -3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 17ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(17 + -3x) = 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 + -3x)' equal to zero and attempt to solve: Simplifying 17 + -3x = 0 Solving 17 + -3x = 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 + -3x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3x = 0 + -17 -3x = 0 + -17 Combine like terms: 0 + -17 = -17 -3x = -17 Add '3x' to each side of the equation. -3x + 3x = -17 + 3x Combine like terms: -3x + 3x = 0 0 = -17 + 3x Simplifying 0 = -17 + 3x 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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