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