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Simplifying Ln(3y + -5) = 2ln(y + -1) + -1ln(y + -1) Reorder the terms: nL(-5 + 3y) = 2ln(y + -1) + -1ln(y + -1) (-5 * nL + 3y * nL) = 2ln(y + -1) + -1ln(y + -1) (-5nL + 3nyL) = 2ln(y + -1) + -1ln(y + -1) Reorder the terms: -5nL + 3nyL = 2ln(-1 + y) + -1ln(y + -1) -5nL + 3nyL = (-1 * 2ln + y * 2ln) + -1ln(y + -1) -5nL + 3nyL = (-2ln + 2lny) + -1ln(y + -1) Reorder the terms: -5nL + 3nyL = -2ln + 2lny + -1ln(-1 + y) -5nL + 3nyL = -2ln + 2lny + (-1 * -1ln + y * -1ln) -5nL + 3nyL = -2ln + 2lny + (1ln + -1lny) Reorder the terms: -5nL + 3nyL = -2ln + 1ln + 2lny + -1lny Combine like terms: -2ln + 1ln = -1ln -5nL + 3nyL = -1ln + 2lny + -1lny Combine like terms: 2lny + -1lny = 1lny -5nL + 3nyL = -1ln + 1lny Solving -5nL + 3nyL = -1ln + 1lny Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add 'ln' to each side of the equation. -5nL + ln + 3nyL = -1ln + ln + 1lny Reorder the terms: ln + -5nL + 3nyL = -1ln + ln + 1lny Combine like terms: -1ln + ln = 0 ln + -5nL + 3nyL = 0 + 1lny ln + -5nL + 3nyL = 1lny Add '-1lny' to each side of the equation. ln + -5nL + -1lny + 3nyL = 1lny + -1lny Reorder the terms: ln + -1lny + -5nL + 3nyL = 1lny + -1lny Combine like terms: 1lny + -1lny = 0 ln + -1lny + -5nL + 3nyL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(l + -1ly + -5L + 3yL) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(l + -1ly + -5L + 3yL)' equal to zero and attempt to solve: Simplifying l + -1ly + -5L + 3yL = 0 Reorder the terms: -5L + l + -1ly + 3yL = 0 Solving -5L + l + -1ly + 3yL = 0 Move all terms containing n to the left, all other terms to the right. Add '5L' to each side of the equation. -5L + l + -1ly + 5L + 3yL = 0 + 5L Reorder the terms: -5L + 5L + l + -1ly + 3yL = 0 + 5L Combine like terms: -5L + 5L = 0 0 + l + -1ly + 3yL = 0 + 5L l + -1ly + 3yL = 0 + 5L Remove the zero: l + -1ly + 3yL = 5L Add '-1l' to each side of the equation. l + -1ly + -1l + 3yL = 5L + -1l Reorder the terms: l + -1l + -1ly + 3yL = 5L + -1l Combine like terms: l + -1l = 0 0 + -1ly + 3yL = 5L + -1l -1ly + 3yL = 5L + -1l Add 'ly' to each side of the equation. -1ly + ly + 3yL = 5L + -1l + ly Combine like terms: -1ly + ly = 0 0 + 3yL = 5L + -1l + ly 3yL = 5L + -1l + ly Add '-3yL' to each side of the equation. 3yL + -3yL = 5L + -1l + ly + -3yL Combine like terms: 3yL + -3yL = 0 0 = 5L + -1l + ly + -3yL Simplifying 0 = 5L + -1l + ly + -3yL The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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