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Simplifying 2ln(x) + ln(x + 7) = 3ln(x + 1) Multiply ln * x 2lnx + ln(x + 7) = 3ln(x + 1) Reorder the terms: 2lnx + ln(7 + x) = 3ln(x + 1) 2lnx + (7 * ln + x * ln) = 3ln(x + 1) 2lnx + (7ln + lnx) = 3ln(x + 1) Reorder the terms: 7ln + 2lnx + lnx = 3ln(x + 1) Combine like terms: 2lnx + lnx = 3lnx 7ln + 3lnx = 3ln(x + 1) Reorder the terms: 7ln + 3lnx = 3ln(1 + x) 7ln + 3lnx = (1 * 3ln + x * 3ln) 7ln + 3lnx = (3ln + 3lnx) Add '-3lnx' to each side of the equation. 7ln + 3lnx + -3lnx = 3ln + 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 7ln + 0 = 3ln + 3lnx + -3lnx 7ln = 3ln + 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 7ln = 3ln + 0 7ln = 3ln Solving 7ln = 3ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 7ln + -3ln = 3ln + -3ln Combine like terms: 7ln + -3ln = 4ln 4ln = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 4ln = 0 Divide each side by '4'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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