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