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Simplifying ln(24 + 2n2) = ln(3n2 + 5n) (24 * ln + 2n2 * ln) = ln(3n2 + 5n) (24ln + 2ln3) = ln(3n2 + 5n) Reorder the terms: 24ln + 2ln3 = ln(5n + 3n2) 24ln + 2ln3 = (5n * ln + 3n2 * ln) 24ln + 2ln3 = (5ln2 + 3ln3) Solving 24ln + 2ln3 = 5ln2 + 3ln3 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln2' to each side of the equation. 24ln + -5ln2 + 2ln3 = 5ln2 + -5ln2 + 3ln3 Combine like terms: 5ln2 + -5ln2 = 0 24ln + -5ln2 + 2ln3 = 0 + 3ln3 24ln + -5ln2 + 2ln3 = 3ln3 Add '-3ln3' to each side of the equation. 24ln + -5ln2 + 2ln3 + -3ln3 = 3ln3 + -3ln3 Combine like terms: 2ln3 + -3ln3 = -1ln3 24ln + -5ln2 + -1ln3 = 3ln3 + -3ln3 Combine like terms: 3ln3 + -3ln3 = 0 24ln + -5ln2 + -1ln3 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(24 + -5n + -1n2) = 0 Factor a trinomial. ln((3 + -1n)(8 + n)) = 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 '(3 + -1n)' equal to zero and attempt to solve: Simplifying 3 + -1n = 0 Solving 3 + -1n = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1n = 0 + -3 -1n = 0 + -3 Combine like terms: 0 + -3 = -3 -1n = -3 Add 'n' to each side of the equation. -1n + n = -3 + n Combine like terms: -1n + n = 0 0 = -3 + n Simplifying 0 = -3 + n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Add '-1n' to each side of the equation. n + -1n = -8 + -1n Combine like terms: n + -1n = 0 0 = -8 + -1n Simplifying 0 = -8 + -1n 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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