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Simplifying ln(2x + 1) = ln(x + -3) + ln(x + 5) Reorder the terms: ln(1 + 2x) = ln(x + -3) + ln(x + 5) (1 * ln + 2x * ln) = ln(x + -3) + ln(x + 5) (1ln + 2lnx) = ln(x + -3) + ln(x + 5) Reorder the terms: 1ln + 2lnx = ln(-3 + x) + ln(x + 5) 1ln + 2lnx = (-3 * ln + x * ln) + ln(x + 5) 1ln + 2lnx = (-3ln + lnx) + ln(x + 5) Reorder the terms: 1ln + 2lnx = -3ln + lnx + ln(5 + x) 1ln + 2lnx = -3ln + lnx + (5 * ln + x * ln) 1ln + 2lnx = -3ln + lnx + (5ln + lnx) Reorder the terms: 1ln + 2lnx = -3ln + 5ln + lnx + lnx Combine like terms: -3ln + 5ln = 2ln 1ln + 2lnx = 2ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = 2ln + 2lnx Add '-2lnx' to each side of the equation. 1ln + 2lnx + -2lnx = 2ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 1ln + 0 = 2ln + 2lnx + -2lnx 1ln = 2ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 1ln = 2ln + 0 1ln = 2ln Solving 1ln = 2ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. 1ln + -2ln = 2ln + -2ln Combine like terms: 1ln + -2ln = -1ln -1ln = 2ln + -2ln Combine like terms: 2ln + -2ln = 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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