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