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