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Simplifying (x + -5) * ln(y + -4) = ln(y + -4) Reorder the terms: (-5 + x) * ln(y + -4) = ln(y + -4) Reorder the terms: (-5 + x) * ln(-4 + y) = ln(y + -4) Reorder the terms for easier multiplication: ln(-5 + x)(-4 + y) = ln(y + -4) Multiply (-5 + x) * (-4 + y) ln(-5(-4 + y) + x(-4 + y)) = ln(y + -4) ln((-4 * -5 + y * -5) + x(-4 + y)) = ln(y + -4) ln((20 + -5y) + x(-4 + y)) = ln(y + -4) ln(20 + -5y + (-4 * x + y * x)) = ln(y + -4) ln(20 + -5y + (-4x + xy)) = ln(y + -4) Reorder the terms: ln(20 + -4x + xy + -5y) = ln(y + -4) ln(20 + -4x + xy + -5y) = ln(y + -4) (20 * ln + -4x * ln + xy * ln + -5y * ln) = ln(y + -4) (20ln + -4lnx + lnxy + -5lny) = ln(y + -4) Reorder the terms: 20ln + -4lnx + lnxy + -5lny = ln(-4 + y) 20ln + -4lnx + lnxy + -5lny = (-4 * ln + y * ln) 20ln + -4lnx + lnxy + -5lny = (-4ln + lny) Solving 20ln + -4lnx + lnxy + -5lny = -4ln + lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4ln' to each side of the equation. 20ln + -4lnx + lnxy + 4ln + -5lny = -4ln + 4ln + lny Reorder the terms: 20ln + 4ln + -4lnx + lnxy + -5lny = -4ln + 4ln + lny Combine like terms: 20ln + 4ln = 24ln 24ln + -4lnx + lnxy + -5lny = -4ln + 4ln + lny Combine like terms: -4ln + 4ln = 0 24ln + -4lnx + lnxy + -5lny = 0 + lny 24ln + -4lnx + lnxy + -5lny = lny Add '-1lny' to each side of the equation. 24ln + -4lnx + lnxy + -5lny + -1lny = lny + -1lny Combine like terms: -5lny + -1lny = -6lny 24ln + -4lnx + lnxy + -6lny = lny + -1lny Combine like terms: lny + -1lny = 0 24ln + -4lnx + lnxy + -6lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(24 + -4x + xy + -6y) = 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 '(24 + -4x + xy + -6y)' equal to zero and attempt to solve: Simplifying 24 + -4x + xy + -6y = 0 Solving 24 + -4x + xy + -6y = 0 Move all terms containing l to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -4x + xy + -24 + -6y = 0 + -24 Reorder the terms: 24 + -24 + -4x + xy + -6y = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -4x + xy + -6y = 0 + -24 -4x + xy + -6y = 0 + -24 Combine like terms: 0 + -24 = -24 -4x + xy + -6y = -24 Add '4x' to each side of the equation. -4x + xy + 4x + -6y = -24 + 4x Reorder the terms: -4x + 4x + xy + -6y = -24 + 4x Combine like terms: -4x + 4x = 0 0 + xy + -6y = -24 + 4x xy + -6y = -24 + 4x Add '-1xy' to each side of the equation. xy + -1xy + -6y = -24 + 4x + -1xy Combine like terms: xy + -1xy = 0 0 + -6y = -24 + 4x + -1xy -6y = -24 + 4x + -1xy Add '6y' to each side of the equation. -6y + 6y = -24 + 4x + -1xy + 6y Combine like terms: -6y + 6y = 0 0 = -24 + 4x + -1xy + 6y Simplifying 0 = -24 + 4x + -1xy + 6y 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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