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Simplifying ln(-2y + 5) + -1ln(y + 4) = ln(-11y + -2) Reorder the terms: ln(5 + -2y) + -1ln(y + 4) = ln(-11y + -2) (5 * ln + -2y * ln) + -1ln(y + 4) = ln(-11y + -2) (5ln + -2lny) + -1ln(y + 4) = ln(-11y + -2) Reorder the terms: 5ln + -2lny + -1ln(4 + y) = ln(-11y + -2) 5ln + -2lny + (4 * -1ln + y * -1ln) = ln(-11y + -2) 5ln + -2lny + (-4ln + -1lny) = ln(-11y + -2) Reorder the terms: 5ln + -4ln + -2lny + -1lny = ln(-11y + -2) Combine like terms: 5ln + -4ln = 1ln 1ln + -2lny + -1lny = ln(-11y + -2) Combine like terms: -2lny + -1lny = -3lny 1ln + -3lny = ln(-11y + -2) Reorder the terms: 1ln + -3lny = ln(-2 + -11y) 1ln + -3lny = (-2 * ln + -11y * ln) 1ln + -3lny = (-2ln + -11lny) Solving 1ln + -3lny = -2ln + -11lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 1ln + 2ln + -3lny = -2ln + 2ln + -11lny Combine like terms: 1ln + 2ln = 3ln 3ln + -3lny = -2ln + 2ln + -11lny Combine like terms: -2ln + 2ln = 0 3ln + -3lny = 0 + -11lny 3ln + -3lny = -11lny Add '11lny' to each side of the equation. 3ln + -3lny + 11lny = -11lny + 11lny Combine like terms: -3lny + 11lny = 8lny 3ln + 8lny = -11lny + 11lny Combine like terms: -11lny + 11lny = 0 3ln + 8lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + 8y) = 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 '(3 + 8y)' equal to zero and attempt to solve: Simplifying 3 + 8y = 0 Solving 3 + 8y = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 8y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8y = 0 + -3 8y = 0 + -3 Combine like terms: 0 + -3 = -3 8y = -3 Add '-8y' to each side of the equation. 8y + -8y = -3 + -8y Combine like terms: 8y + -8y = 0 0 = -3 + -8y Simplifying 0 = -3 + -8y 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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