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Simplifying ln(3n2 + -5n) = ln(14 + -2n2) Reorder the terms: ln(-5n + 3n2) = ln(14 + -2n2) (-5n * ln + 3n2 * ln) = ln(14 + -2n2) (-5ln2 + 3ln3) = ln(14 + -2n2) -5ln2 + 3ln3 = (14 * ln + -2n2 * ln) -5ln2 + 3ln3 = (14ln + -2ln3) Solving -5ln2 + 3ln3 = 14ln + -2ln3 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. -5ln2 + -14ln + 3ln3 = 14ln + -14ln + -2ln3 Reorder the terms: -14ln + -5ln2 + 3ln3 = 14ln + -14ln + -2ln3 Combine like terms: 14ln + -14ln = 0 -14ln + -5ln2 + 3ln3 = 0 + -2ln3 -14ln + -5ln2 + 3ln3 = -2ln3 Add '2ln3' to each side of the equation. -14ln + -5ln2 + 3ln3 + 2ln3 = -2ln3 + 2ln3 Combine like terms: 3ln3 + 2ln3 = 5ln3 -14ln + -5ln2 + 5ln3 = -2ln3 + 2ln3 Combine like terms: -2ln3 + 2ln3 = 0 -14ln + -5ln2 + 5ln3 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-14 + -5n + 5n2) = 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 '(-14 + -5n + 5n2)' equal to zero and attempt to solve: Simplifying -14 + -5n + 5n2 = 0 Solving -14 + -5n + 5n2 = 0 Move all terms containing l to the left, all other terms to the right. Add '14' to each side of the equation. -14 + -5n + 14 + 5n2 = 0 + 14 Reorder the terms: -14 + 14 + -5n + 5n2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -5n + 5n2 = 0 + 14 -5n + 5n2 = 0 + 14 Combine like terms: 0 + 14 = 14 -5n + 5n2 = 14 Add '5n' to each side of the equation. -5n + 5n + 5n2 = 14 + 5n Combine like terms: -5n + 5n = 0 0 + 5n2 = 14 + 5n 5n2 = 14 + 5n Add '-5n2' to each side of the equation. 5n2 + -5n2 = 14 + 5n + -5n2 Combine like terms: 5n2 + -5n2 = 0 0 = 14 + 5n + -5n2 Simplifying 0 = 14 + 5n + -5n2 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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