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Simplifying ln(2y + -1) + -1ln(y + -4) = ln(-1y + 15) Reorder the terms: ln(-1 + 2y) + -1ln(y + -4) = ln(-1y + 15) (-1 * ln + 2y * ln) + -1ln(y + -4) = ln(-1y + 15) (-1ln + 2lny) + -1ln(y + -4) = ln(-1y + 15) Reorder the terms: -1ln + 2lny + -1ln(-4 + y) = ln(-1y + 15) -1ln + 2lny + (-4 * -1ln + y * -1ln) = ln(-1y + 15) -1ln + 2lny + (4ln + -1lny) = ln(-1y + 15) Reorder the terms: -1ln + 4ln + 2lny + -1lny = ln(-1y + 15) Combine like terms: -1ln + 4ln = 3ln 3ln + 2lny + -1lny = ln(-1y + 15) Combine like terms: 2lny + -1lny = 1lny 3ln + 1lny = ln(-1y + 15) Reorder the terms: 3ln + 1lny = ln(15 + -1y) 3ln + 1lny = (15 * ln + -1y * ln) 3ln + 1lny = (15ln + -1lny) Solving 3ln + 1lny = 15ln + -1lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. 3ln + -15ln + 1lny = 15ln + -15ln + -1lny Combine like terms: 3ln + -15ln = -12ln -12ln + 1lny = 15ln + -15ln + -1lny Combine like terms: 15ln + -15ln = 0 -12ln + 1lny = 0 + -1lny -12ln + 1lny = -1lny Add 'lny' to each side of the equation. -12ln + 1lny + lny = -1lny + lny Combine like terms: 1lny + lny = 2lny -12ln + 2lny = -1lny + lny Combine like terms: -1lny + lny = 0 -12ln + 2lny = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-6 + y) = 0 Ignore the factor 2.Subproblem 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 '(-6 + y)' equal to zero and attempt to solve: Simplifying -6 + y = 0 Solving -6 + y = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 0 + 6 Combine like terms: -6 + 6 = 0 0 + y = 0 + 6 y = 0 + 6 Combine like terms: 0 + 6 = 6 y = 6 Add '-1y' to each side of the equation. y + -1y = 6 + -1y Combine like terms: y + -1y = 0 0 = 6 + -1y Simplifying 0 = 6 + -1y 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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