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Simplifying ln(x + -1) + ln(x + 2) = ln(6x + -8) Reorder the terms: ln(-1 + x) + ln(x + 2) = ln(6x + -8) (-1 * ln + x * ln) + ln(x + 2) = ln(6x + -8) (-1ln + lnx) + ln(x + 2) = ln(6x + -8) Reorder the terms: -1ln + lnx + ln(2 + x) = ln(6x + -8) -1ln + lnx + (2 * ln + x * ln) = ln(6x + -8) -1ln + lnx + (2ln + lnx) = ln(6x + -8) Reorder the terms: -1ln + 2ln + lnx + lnx = ln(6x + -8) Combine like terms: -1ln + 2ln = 1ln 1ln + lnx + lnx = ln(6x + -8) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(6x + -8) Reorder the terms: 1ln + 2lnx = ln(-8 + 6x) 1ln + 2lnx = (-8 * ln + 6x * ln) 1ln + 2lnx = (-8ln + 6lnx) Solving 1ln + 2lnx = -8ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8ln' to each side of the equation. 1ln + 8ln + 2lnx = -8ln + 8ln + 6lnx Combine like terms: 1ln + 8ln = 9ln 9ln + 2lnx = -8ln + 8ln + 6lnx Combine like terms: -8ln + 8ln = 0 9ln + 2lnx = 0 + 6lnx 9ln + 2lnx = 6lnx Add '-6lnx' to each side of the equation. 9ln + 2lnx + -6lnx = 6lnx + -6lnx Combine like terms: 2lnx + -6lnx = -4lnx 9ln + -4lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 9ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + -4x) = 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 '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Add '4x' to each side of the equation. -4x + 4x = -9 + 4x Combine like terms: -4x + 4x = 0 0 = -9 + 4x Simplifying 0 = -9 + 4x 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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