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