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Simplifying ln(2t + 7) = ln(3) + -1ln(t + 1) Reorder the terms: ln(7 + 2t) = ln(3) + -1ln(t + 1) (7 * ln + 2t * ln) = ln(3) + -1ln(t + 1) (7ln + 2lnt) = ln(3) + -1ln(t + 1) Reorder the terms for easier multiplication: 7ln + 2lnt = 3ln + -1ln(t + 1) Reorder the terms: 7ln + 2lnt = 3ln + -1ln(1 + t) 7ln + 2lnt = 3ln + (1 * -1ln + t * -1ln) 7ln + 2lnt = 3ln + (-1ln + -1lnt) Combine like terms: 3ln + -1ln = 2ln 7ln + 2lnt = 2ln + -1lnt Solving 7ln + 2lnt = 2ln + -1lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. 7ln + -2ln + 2lnt = 2ln + -2ln + -1lnt Combine like terms: 7ln + -2ln = 5ln 5ln + 2lnt = 2ln + -2ln + -1lnt Combine like terms: 2ln + -2ln = 0 5ln + 2lnt = 0 + -1lnt 5ln + 2lnt = -1lnt Add 'lnt' to each side of the equation. 5ln + 2lnt + lnt = -1lnt + lnt Combine like terms: 2lnt + lnt = 3lnt 5ln + 3lnt = -1lnt + lnt Combine like terms: -1lnt + lnt = 0 5ln + 3lnt = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + 3t) = 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 '(5 + 3t)' equal to zero and attempt to solve: Simplifying 5 + 3t = 0 Solving 5 + 3t = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3t = 0 + -5 3t = 0 + -5 Combine like terms: 0 + -5 = -5 3t = -5 Add '-3t' to each side of the equation. 3t + -3t = -5 + -3t Combine like terms: 3t + -3t = 0 0 = -5 + -3t Simplifying 0 = -5 + -3t 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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