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Simplifying ln(x + 2) = 7 + ln(x + -1) Reorder the terms: ln(2 + x) = 7 + ln(x + -1) (2 * ln + x * ln) = 7 + ln(x + -1) (2ln + lnx) = 7 + ln(x + -1) Reorder the terms: 2ln + lnx = 7 + ln(-1 + x) 2ln + lnx = 7 + (-1 * ln + x * ln) 2ln + lnx = 7 + (-1ln + lnx) Add '-1lnx' to each side of the equation. 2ln + lnx + -1lnx = 7 + -1ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 2ln + 0 = 7 + -1ln + lnx + -1lnx 2ln = 7 + -1ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 2ln = 7 + -1ln + 0 2ln = 7 + -1ln Solving 2ln = 7 + -1ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 2ln + ln = 7 + -1ln + ln Combine like terms: 2ln + ln = 3ln 3ln = 7 + -1ln + ln Combine like terms: -1ln + ln = 0 3ln = 7 + 0 3ln = 7 Divide each side by '3n'. l = 2.333333333n-1 Simplifying l = 2.333333333n-1
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