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Simplifying ln(x + 3) + ln(x + 1) = 2ln(2x + 2) Reorder the terms: ln(3 + x) + ln(x + 1) = 2ln(2x + 2) (3 * ln + x * ln) + ln(x + 1) = 2ln(2x + 2) (3ln + lnx) + ln(x + 1) = 2ln(2x + 2) Reorder the terms: 3ln + lnx + ln(1 + x) = 2ln(2x + 2) 3ln + lnx + (1 * ln + x * ln) = 2ln(2x + 2) 3ln + lnx + (1ln + lnx) = 2ln(2x + 2) Reorder the terms: 3ln + 1ln + lnx + lnx = 2ln(2x + 2) Combine like terms: 3ln + 1ln = 4ln 4ln + lnx + lnx = 2ln(2x + 2) Combine like terms: lnx + lnx = 2lnx 4ln + 2lnx = 2ln(2x + 2) Reorder the terms: 4ln + 2lnx = 2ln(2 + 2x) 4ln + 2lnx = (2 * 2ln + 2x * 2ln) 4ln + 2lnx = (4ln + 4lnx) Add '-4ln' to each side of the equation. 4ln + -4ln + 2lnx = 4ln + -4ln + 4lnx Combine like terms: 4ln + -4ln = 0 0 + 2lnx = 4ln + -4ln + 4lnx 2lnx = 4ln + -4ln + 4lnx Combine like terms: 4ln + -4ln = 0 2lnx = 0 + 4lnx 2lnx = 4lnx Solving 2lnx = 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4lnx' to each side of the equation. 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -2lnx = 0 Divide each side by '-2'. lnx = 0 Simplifying lnx = 0 The solution to this equation could not be determined.
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