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Simplifying ln(-3y + 6) + -1ln(y + 2) = ln(-9y + -12) Reorder the terms: ln(6 + -3y) + -1ln(y + 2) = ln(-9y + -12) (6 * ln + -3y * ln) + -1ln(y + 2) = ln(-9y + -12) (6ln + -3lny) + -1ln(y + 2) = ln(-9y + -12) Reorder the terms: 6ln + -3lny + -1ln(2 + y) = ln(-9y + -12) 6ln + -3lny + (2 * -1ln + y * -1ln) = ln(-9y + -12) 6ln + -3lny + (-2ln + -1lny) = ln(-9y + -12) Reorder the terms: 6ln + -2ln + -3lny + -1lny = ln(-9y + -12) Combine like terms: 6ln + -2ln = 4ln 4ln + -3lny + -1lny = ln(-9y + -12) Combine like terms: -3lny + -1lny = -4lny 4ln + -4lny = ln(-9y + -12) Reorder the terms: 4ln + -4lny = ln(-12 + -9y) 4ln + -4lny = (-12 * ln + -9y * ln) 4ln + -4lny = (-12ln + -9lny) Solving 4ln + -4lny = -12ln + -9lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. 4ln + 12ln + -4lny = -12ln + 12ln + -9lny Combine like terms: 4ln + 12ln = 16ln 16ln + -4lny = -12ln + 12ln + -9lny Combine like terms: -12ln + 12ln = 0 16ln + -4lny = 0 + -9lny 16ln + -4lny = -9lny Add '9lny' to each side of the equation. 16ln + -4lny + 9lny = -9lny + 9lny Combine like terms: -4lny + 9lny = 5lny 16ln + 5lny = -9lny + 9lny Combine like terms: -9lny + 9lny = 0 16ln + 5lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(16 + 5y) = 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 '(16 + 5y)' equal to zero and attempt to solve: Simplifying 16 + 5y = 0 Solving 16 + 5y = 0 Move all terms containing l to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + 5y = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 5y = 0 + -16 5y = 0 + -16 Combine like terms: 0 + -16 = -16 5y = -16 Add '-5y' to each side of the equation. 5y + -5y = -16 + -5y Combine like terms: 5y + -5y = 0 0 = -16 + -5y Simplifying 0 = -16 + -5y 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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