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Simplifying lnx + ln(x + 3) = ln(x + 5) + ln(x + 1) Reorder the terms: lnx + ln(3 + x) = ln(x + 5) + ln(x + 1) lnx + (3 * ln + x * ln) = ln(x + 5) + ln(x + 1) lnx + (3ln + lnx) = ln(x + 5) + ln(x + 1) Reorder the terms: 3ln + lnx + lnx = ln(x + 5) + ln(x + 1) Combine like terms: lnx + lnx = 2lnx 3ln + 2lnx = ln(x + 5) + ln(x + 1) Reorder the terms: 3ln + 2lnx = ln(5 + x) + ln(x + 1) 3ln + 2lnx = (5 * ln + x * ln) + ln(x + 1) 3ln + 2lnx = (5ln + lnx) + ln(x + 1) Reorder the terms: 3ln + 2lnx = 5ln + lnx + ln(1 + x) 3ln + 2lnx = 5ln + lnx + (1 * ln + x * ln) 3ln + 2lnx = 5ln + lnx + (1ln + lnx) Reorder the terms: 3ln + 2lnx = 5ln + 1ln + lnx + lnx Combine like terms: 5ln + 1ln = 6ln 3ln + 2lnx = 6ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx 3ln + 2lnx = 6ln + 2lnx Add '-2lnx' to each side of the equation. 3ln + 2lnx + -2lnx = 6ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 3ln + 0 = 6ln + 2lnx + -2lnx 3ln = 6ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 3ln = 6ln + 0 3ln = 6ln Solving 3ln = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 3ln + -6ln = 6ln + -6ln Combine like terms: 3ln + -6ln = -3ln -3ln = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -3ln = 0 Divide each side by '-3'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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