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Simplifying ln(x + 1) = 3ln(x + 2) + -2ln(x + 3) Reorder the terms: ln(1 + x) = 3ln(x + 2) + -2ln(x + 3) (1 * ln + x * ln) = 3ln(x + 2) + -2ln(x + 3) (1ln + lnx) = 3ln(x + 2) + -2ln(x + 3) Reorder the terms: 1ln + lnx = 3ln(2 + x) + -2ln(x + 3) 1ln + lnx = (2 * 3ln + x * 3ln) + -2ln(x + 3) 1ln + lnx = (6ln + 3lnx) + -2ln(x + 3) Reorder the terms: 1ln + lnx = 6ln + 3lnx + -2ln(3 + x) 1ln + lnx = 6ln + 3lnx + (3 * -2ln + x * -2ln) 1ln + lnx = 6ln + 3lnx + (-6ln + -2lnx) Reorder the terms: 1ln + lnx = 6ln + -6ln + 3lnx + -2lnx Combine like terms: 6ln + -6ln = 0 1ln + lnx = 0 + 3lnx + -2lnx 1ln + lnx = 3lnx + -2lnx Combine like terms: 3lnx + -2lnx = 1lnx 1ln + lnx = 1lnx Solving 1ln + lnx = 1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 1ln + lnx + -1lnx = 1lnx + -1lnx Combine like terms: lnx + -1lnx = 0 1ln + 0 = 1lnx + -1lnx 1ln = 1lnx + -1lnx Combine like terms: 1lnx + -1lnx = 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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