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Simplifying ln(m + 7) = ln(3m + -5) Reorder the terms: ln(7 + m) = ln(3m + -5) (7 * ln + m * ln) = ln(3m + -5) Reorder the terms: (lmn + 7ln) = ln(3m + -5) (lmn + 7ln) = ln(3m + -5) Reorder the terms: lmn + 7ln = ln(-5 + 3m) lmn + 7ln = (-5 * ln + 3m * ln) Reorder the terms: lmn + 7ln = (3lmn + -5ln) lmn + 7ln = (3lmn + -5ln) Solving lmn + 7ln = 3lmn + -5ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3lmn' to each side of the equation. lmn + -3lmn + 7ln = 3lmn + -3lmn + -5ln Combine like terms: lmn + -3lmn = -2lmn -2lmn + 7ln = 3lmn + -3lmn + -5ln Combine like terms: 3lmn + -3lmn = 0 -2lmn + 7ln = 0 + -5ln -2lmn + 7ln = -5ln Add '5ln' to each side of the equation. -2lmn + 7ln + 5ln = -5ln + 5ln Combine like terms: 7ln + 5ln = 12ln -2lmn + 12ln = -5ln + 5ln Combine like terms: -5ln + 5ln = 0 -2lmn + 12ln = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-1m + 6) = 0 Ignore the factor 2.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 '(-1m + 6)' equal to zero and attempt to solve: Simplifying -1m + 6 = 0 Reorder the terms: 6 + -1m = 0 Solving 6 + -1m = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1m = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1m = 0 + -6 -1m = 0 + -6 Combine like terms: 0 + -6 = -6 -1m = -6 Add 'm' to each side of the equation. -1m + m = -6 + m Combine like terms: -1m + m = 0 0 = -6 + m Simplifying 0 = -6 + m 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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