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