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Simplifying 5ln(t + 1) = 3ln(t + 1) + 3 Reorder the terms: 5ln(1 + t) = 3ln(t + 1) + 3 (1 * 5ln + t * 5ln) = 3ln(t + 1) + 3 (5ln + 5lnt) = 3ln(t + 1) + 3 Reorder the terms: 5ln + 5lnt = 3ln(1 + t) + 3 5ln + 5lnt = (1 * 3ln + t * 3ln) + 3 5ln + 5lnt = (3ln + 3lnt) + 3 Reorder the terms: 5ln + 5lnt = 3 + 3ln + 3lnt Solving 5ln + 5lnt = 3 + 3ln + 3lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 5ln + -3ln + 5lnt = 3 + 3ln + -3ln + 3lnt Combine like terms: 5ln + -3ln = 2ln 2ln + 5lnt = 3 + 3ln + -3ln + 3lnt Combine like terms: 3ln + -3ln = 0 2ln + 5lnt = 3 + 0 + 3lnt 2ln + 5lnt = 3 + 3lnt Add '-3lnt' to each side of the equation. 2ln + 5lnt + -3lnt = 3 + 3lnt + -3lnt Combine like terms: 5lnt + -3lnt = 2lnt 2ln + 2lnt = 3 + 3lnt + -3lnt Combine like terms: 3lnt + -3lnt = 0 2ln + 2lnt = 3 + 0 2ln + 2lnt = 3 Reorder the terms: -3 + 2ln + 2lnt = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 2ln + 2lnt = 0 The solution to this equation could not be determined.
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