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Simplifying ln(3x + -9) = ln(2n + 6) Reorder the terms: ln(-9 + 3x) = ln(2n + 6) (-9 * ln + 3x * ln) = ln(2n + 6) (-9ln + 3lnx) = ln(2n + 6) Reorder the terms: -9ln + 3lnx = ln(6 + 2n) -9ln + 3lnx = (6 * ln + 2n * ln) -9ln + 3lnx = (6ln + 2ln2) Solving -9ln + 3lnx = 6ln + 2ln2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -9ln + -6ln + 3lnx = 6ln + -6ln + 2ln2 Combine like terms: -9ln + -6ln = -15ln -15ln + 3lnx = 6ln + -6ln + 2ln2 Combine like terms: 6ln + -6ln = 0 -15ln + 3lnx = 0 + 2ln2 -15ln + 3lnx = 2ln2 Add '-2ln2' to each side of the equation. -15ln + 3lnx + -2ln2 = 2ln2 + -2ln2 Combine like terms: 2ln2 + -2ln2 = 0 -15ln + 3lnx + -2ln2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + 3x + -2n) = 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 '(-15 + 3x + -2n)' equal to zero and attempt to solve: Simplifying -15 + 3x + -2n = 0 Reorder the terms: -15 + -2n + 3x = 0 Solving -15 + -2n + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + -2n + 15 + 3x = 0 + 15 Reorder the terms: -15 + 15 + -2n + 3x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2n + 3x = 0 + 15 -2n + 3x = 0 + 15 Combine like terms: 0 + 15 = 15 -2n + 3x = 15 Add '2n' to each side of the equation. -2n + 2n + 3x = 15 + 2n Combine like terms: -2n + 2n = 0 0 + 3x = 15 + 2n 3x = 15 + 2n Add '-3x' to each side of the equation. 3x + -3x = 15 + 2n + -3x Combine like terms: 3x + -3x = 0 0 = 15 + 2n + -3x Simplifying 0 = 15 + 2n + -3x 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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