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Simplifying ln(2n + 6) = ln(-5n + -1) Reorder the terms: ln(6 + 2n) = ln(-5n + -1) (6 * ln + 2n * ln) = ln(-5n + -1) (6ln + 2ln2) = ln(-5n + -1) Reorder the terms: 6ln + 2ln2 = ln(-1 + -5n) 6ln + 2ln2 = (-1 * ln + -5n * ln) 6ln + 2ln2 = (-1ln + -5ln2) Solving 6ln + 2ln2 = -1ln + -5ln2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 6ln + ln + 2ln2 = -1ln + ln + -5ln2 Combine like terms: 6ln + ln = 7ln 7ln + 2ln2 = -1ln + ln + -5ln2 Combine like terms: -1ln + ln = 0 7ln + 2ln2 = 0 + -5ln2 7ln + 2ln2 = -5ln2 Add '5ln2' to each side of the equation. 7ln + 2ln2 + 5ln2 = -5ln2 + 5ln2 Combine like terms: 2ln2 + 5ln2 = 7ln2 7ln + 7ln2 = -5ln2 + 5ln2 Combine like terms: -5ln2 + 5ln2 = 0 7ln + 7ln2 = 0 Factor out the Greatest Common Factor (GCF), '7ln'. 7ln(1 + n) = 0 Ignore the factor 7.Subproblem 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 '(1 + n)' equal to zero and attempt to solve: Simplifying 1 + n = 0 Solving 1 + n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + n = 0 + -1 n = 0 + -1 Combine like terms: 0 + -1 = -1 n = -1 Add '-1n' to each side of the equation. n + -1n = -1 + -1n Combine like terms: n + -1n = 0 0 = -1 + -1n Simplifying 0 = -1 + -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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