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Simplifying 8ln(3y + 1) + -8ln(y + 3) = 2x Reorder the terms: 8ln(1 + 3y) + -8ln(y + 3) = 2x (1 * 8ln + 3y * 8ln) + -8ln(y + 3) = 2x (8ln + 24lny) + -8ln(y + 3) = 2x Reorder the terms: 8ln + 24lny + -8ln(3 + y) = 2x 8ln + 24lny + (3 * -8ln + y * -8ln) = 2x 8ln + 24lny + (-24ln + -8lny) = 2x Reorder the terms: 8ln + -24ln + 24lny + -8lny = 2x Combine like terms: 8ln + -24ln = -16ln -16ln + 24lny + -8lny = 2x Combine like terms: 24lny + -8lny = 16lny -16ln + 16lny = 2x Solving -16ln + 16lny = 2x Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Combine like terms: 2x + -2x = 0 -16ln + 16lny + -2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8ln + 8lny + -1x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8ln + 8lny + -1x)' equal to zero and attempt to solve: Simplifying -8ln + 8lny + -1x = 0 Solving -8ln + 8lny + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add 'x' to each side of the equation. -8ln + 8lny + -1x + x = 0 + x Combine like terms: -1x + x = 0 -8ln + 8lny + 0 = 0 + x -8ln + 8lny = 0 + x Remove the zero: -8ln + 8lny = x 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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