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Simplifying ln(3x + -2) + 2 = 2ln(x + 2) Reorder the terms: ln(-2 + 3x) + 2 = 2ln(x + 2) (-2 * ln + 3x * ln) + 2 = 2ln(x + 2) (-2ln + 3lnx) + 2 = 2ln(x + 2) Reorder the terms: 2 + -2ln + 3lnx = 2ln(x + 2) Reorder the terms: 2 + -2ln + 3lnx = 2ln(2 + x) 2 + -2ln + 3lnx = (2 * 2ln + x * 2ln) 2 + -2ln + 3lnx = (4ln + 2lnx) Solving 2 + -2ln + 3lnx = 4ln + 2lnx 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. 2 + -2ln + -4ln + 3lnx = 4ln + -4ln + 2lnx Combine like terms: -2ln + -4ln = -6ln 2 + -6ln + 3lnx = 4ln + -4ln + 2lnx Combine like terms: 4ln + -4ln = 0 2 + -6ln + 3lnx = 0 + 2lnx 2 + -6ln + 3lnx = 2lnx Add '-2lnx' to each side of the equation. 2 + -6ln + 3lnx + -2lnx = 2lnx + -2lnx Combine like terms: 3lnx + -2lnx = 1lnx 2 + -6ln + 1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 2 + -6ln + 1lnx = 0 Add '-2' to each side of the equation. 2 + -6ln + -2 + 1lnx = 0 + -2 Reorder the terms: 2 + -2 + -6ln + 1lnx = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6ln + 1lnx = 0 + -2 -6ln + 1lnx = 0 + -2 Combine like terms: 0 + -2 = -2 -6ln + 1lnx = -2 Reorder the terms: 2 + -6ln + 1lnx = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -6ln + 1lnx = 0 The solution to this equation could not be determined.
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