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Simplifying ln(x + -1) + -1ln(x + -2) = lnx2 Reorder the terms: ln(-1 + x) + -1ln(x + -2) = lnx2 (-1 * ln + x * ln) + -1ln(x + -2) = lnx2 (-1ln + lnx) + -1ln(x + -2) = lnx2 Reorder the terms: -1ln + lnx + -1ln(-2 + x) = lnx2 -1ln + lnx + (-2 * -1ln + x * -1ln) = lnx2 -1ln + lnx + (2ln + -1lnx) = lnx2 Reorder the terms: -1ln + 2ln + lnx + -1lnx = lnx2 Combine like terms: -1ln + 2ln = 1ln 1ln + lnx + -1lnx = lnx2 Combine like terms: lnx + -1lnx = 0 1ln + 0 = lnx2 1ln = lnx2 Solving 1ln = lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx2' to each side of the equation. 1ln + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 1ln + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -1x2) = 0 Factor a difference between two squares. ln((1 + x)(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 + 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 + -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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