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Simplifying ln(1 + y) + -1ln(y) = ln(x + 1) + -2ln(x + -1) (1 * ln + y * ln) + -1ln(y) = ln(x + 1) + -2ln(x + -1) (1ln + lny) + -1ln(y) = ln(x + 1) + -2ln(x + -1) Multiply ln * y 1ln + lny + -1lny = ln(x + 1) + -2ln(x + -1) Combine like terms: lny + -1lny = 0 1ln + 0 = ln(x + 1) + -2ln(x + -1) 1ln = ln(x + 1) + -2ln(x + -1) Reorder the terms: 1ln = ln(1 + x) + -2ln(x + -1) 1ln = (1 * ln + x * ln) + -2ln(x + -1) 1ln = (1ln + lnx) + -2ln(x + -1) Reorder the terms: 1ln = 1ln + lnx + -2ln(-1 + x) 1ln = 1ln + lnx + (-1 * -2ln + x * -2ln) 1ln = 1ln + lnx + (2ln + -2lnx) Reorder the terms: 1ln = 1ln + 2ln + lnx + -2lnx Combine like terms: 1ln + 2ln = 3ln 1ln = 3ln + lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx 1ln = 3ln + -1lnx Solving 1ln = 3ln + -1lnx 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 = 3ln + -3ln + -1lnx Combine like terms: 1ln + -3ln = -2ln -2ln = 3ln + -3ln + -1lnx Combine like terms: 3ln + -3ln = 0 -2ln = 0 + -1lnx -2ln = -1lnx Add 'lnx' to each side of the equation. -2ln + lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -2ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -1x 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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