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Simplifying (x + -1) * ln(x + 1) = 0 Reorder the terms: (-1 + x) * ln(x + 1) = 0 Reorder the terms: (-1 + x) * ln(1 + x) = 0 Reorder the terms for easier multiplication: ln(-1 + x)(1 + x) = 0 Multiply (-1 + x) * (1 + x) ln(-1(1 + x) + x(1 + x)) = 0 ln((1 * -1 + x * -1) + x(1 + x)) = 0 ln((-1 + -1x) + x(1 + x)) = 0 ln(-1 + -1x + (1 * x + x * x)) = 0 ln(-1 + -1x + (1x + x2)) = 0 Combine like terms: -1x + 1x = 0 ln(-1 + 0 + x2) = 0 ln(-1 + x2) = 0 (-1 * ln + x2 * ln) = 0 (-1ln + lnx2) = 0 Solving -1ln + lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1 + x2) = 0 Factor a difference between two squares. ln((1 + x)(-1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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