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Simplifying ln(-4y + 8) + -1ln(y + 7) = ln(-12y + 13) Reorder the terms: ln(8 + -4y) + -1ln(y + 7) = ln(-12y + 13) (8 * ln + -4y * ln) + -1ln(y + 7) = ln(-12y + 13) (8ln + -4lny) + -1ln(y + 7) = ln(-12y + 13) Reorder the terms: 8ln + -4lny + -1ln(7 + y) = ln(-12y + 13) 8ln + -4lny + (7 * -1ln + y * -1ln) = ln(-12y + 13) 8ln + -4lny + (-7ln + -1lny) = ln(-12y + 13) Reorder the terms: 8ln + -7ln + -4lny + -1lny = ln(-12y + 13) Combine like terms: 8ln + -7ln = 1ln 1ln + -4lny + -1lny = ln(-12y + 13) Combine like terms: -4lny + -1lny = -5lny 1ln + -5lny = ln(-12y + 13) Reorder the terms: 1ln + -5lny = ln(13 + -12y) 1ln + -5lny = (13 * ln + -12y * ln) 1ln + -5lny = (13ln + -12lny) Solving 1ln + -5lny = 13ln + -12lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-13ln' to each side of the equation. 1ln + -13ln + -5lny = 13ln + -13ln + -12lny Combine like terms: 1ln + -13ln = -12ln -12ln + -5lny = 13ln + -13ln + -12lny Combine like terms: 13ln + -13ln = 0 -12ln + -5lny = 0 + -12lny -12ln + -5lny = -12lny Add '12lny' to each side of the equation. -12ln + -5lny + 12lny = -12lny + 12lny Combine like terms: -5lny + 12lny = 7lny -12ln + 7lny = -12lny + 12lny Combine like terms: -12lny + 12lny = 0 -12ln + 7lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-12 + 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 '(-12 + 7y)' equal to zero and attempt to solve: Simplifying -12 + 7y = 0 Solving -12 + 7y = 0 Move all terms containing l to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + 7y = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 7y = 0 + 12 7y = 0 + 12 Combine like terms: 0 + 12 = 12 7y = 12 Add '-7y' to each side of the equation. 7y + -7y = 12 + -7y Combine like terms: 7y + -7y = 0 0 = 12 + -7y Simplifying 0 = 12 + -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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