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Simplifying ln(-2y + 4) + -1ln(y + 5) = ln(-10y + 18) Reorder the terms: ln(4 + -2y) + -1ln(y + 5) = ln(-10y + 18) (4 * ln + -2y * ln) + -1ln(y + 5) = ln(-10y + 18) (4ln + -2lny) + -1ln(y + 5) = ln(-10y + 18) Reorder the terms: 4ln + -2lny + -1ln(5 + y) = ln(-10y + 18) 4ln + -2lny + (5 * -1ln + y * -1ln) = ln(-10y + 18) 4ln + -2lny + (-5ln + -1lny) = ln(-10y + 18) Reorder the terms: 4ln + -5ln + -2lny + -1lny = ln(-10y + 18) Combine like terms: 4ln + -5ln = -1ln -1ln + -2lny + -1lny = ln(-10y + 18) Combine like terms: -2lny + -1lny = -3lny -1ln + -3lny = ln(-10y + 18) Reorder the terms: -1ln + -3lny = ln(18 + -10y) -1ln + -3lny = (18 * ln + -10y * ln) -1ln + -3lny = (18ln + -10lny) Solving -1ln + -3lny = 18ln + -10lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. -1ln + -18ln + -3lny = 18ln + -18ln + -10lny Combine like terms: -1ln + -18ln = -19ln -19ln + -3lny = 18ln + -18ln + -10lny Combine like terms: 18ln + -18ln = 0 -19ln + -3lny = 0 + -10lny -19ln + -3lny = -10lny Add '10lny' to each side of the equation. -19ln + -3lny + 10lny = -10lny + 10lny Combine like terms: -3lny + 10lny = 7lny -19ln + 7lny = -10lny + 10lny Combine like terms: -10lny + 10lny = 0 -19ln + 7lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-19 + 7y) = 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 '(-19 + 7y)' equal to zero and attempt to solve: Simplifying -19 + 7y = 0 Solving -19 + 7y = 0 Move all terms containing l to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 7y = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 7y = 0 + 19 7y = 0 + 19 Combine like terms: 0 + 19 = 19 7y = 19 Add '-7y' to each side of the equation. 7y + -7y = 19 + -7y Combine like terms: 7y + -7y = 0 0 = 19 + -7y Simplifying 0 = 19 + -7y 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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