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Simplifying ln(3x + 5) + ln(x + 1) = 2ln(2x + 2) Reorder the terms: ln(5 + 3x) + ln(x + 1) = 2ln(2x + 2) (5 * ln + 3x * ln) + ln(x + 1) = 2ln(2x + 2) (5ln + 3lnx) + ln(x + 1) = 2ln(2x + 2) Reorder the terms: 5ln + 3lnx + ln(1 + x) = 2ln(2x + 2) 5ln + 3lnx + (1 * ln + x * ln) = 2ln(2x + 2) 5ln + 3lnx + (1ln + lnx) = 2ln(2x + 2) Reorder the terms: 5ln + 1ln + 3lnx + lnx = 2ln(2x + 2) Combine like terms: 5ln + 1ln = 6ln 6ln + 3lnx + lnx = 2ln(2x + 2) Combine like terms: 3lnx + lnx = 4lnx 6ln + 4lnx = 2ln(2x + 2) Reorder the terms: 6ln + 4lnx = 2ln(2 + 2x) 6ln + 4lnx = (2 * 2ln + 2x * 2ln) 6ln + 4lnx = (4ln + 4lnx) Add '-4lnx' to each side of the equation. 6ln + 4lnx + -4lnx = 4ln + 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 6ln + 0 = 4ln + 4lnx + -4lnx 6ln = 4ln + 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 6ln = 4ln + 0 6ln = 4ln Solving 6ln = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 6ln + -4ln = 4ln + -4ln Combine like terms: 6ln + -4ln = 2ln 2ln = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 2ln = 0 Divide each side by '2'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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