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