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