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Simplifying ln(x + -2) + -1(x + 5) = ln(x + -1) + -1(x + 8) Reorder the terms: ln(-2 + x) + -1(x + 5) = ln(x + -1) + -1(x + 8) (-2 * ln + x * ln) + -1(x + 5) = ln(x + -1) + -1(x + 8) (-2ln + lnx) + -1(x + 5) = ln(x + -1) + -1(x + 8) Reorder the terms: -2ln + lnx + -1(5 + x) = ln(x + -1) + -1(x + 8) -2ln + lnx + (5 * -1 + x * -1) = ln(x + -1) + -1(x + 8) -2ln + lnx + (-5 + -1x) = ln(x + -1) + -1(x + 8) Reorder the terms: -5 + -2ln + lnx + -1x = ln(x + -1) + -1(x + 8) Reorder the terms: -5 + -2ln + lnx + -1x = ln(-1 + x) + -1(x + 8) -5 + -2ln + lnx + -1x = (-1 * ln + x * ln) + -1(x + 8) -5 + -2ln + lnx + -1x = (-1ln + lnx) + -1(x + 8) Reorder the terms: -5 + -2ln + lnx + -1x = -1ln + lnx + -1(8 + x) -5 + -2ln + lnx + -1x = -1ln + lnx + (8 * -1 + x * -1) -5 + -2ln + lnx + -1x = -1ln + lnx + (-8 + -1x) Reorder the terms: -5 + -2ln + lnx + -1x = -8 + -1ln + lnx + -1x Add '-1lnx' to each side of the equation. -5 + -2ln + lnx + -1lnx + -1x = -8 + -1ln + lnx + -1lnx + -1x Combine like terms: lnx + -1lnx = 0 -5 + -2ln + 0 + -1x = -8 + -1ln + lnx + -1lnx + -1x -5 + -2ln + -1x = -8 + -1ln + lnx + -1lnx + -1x Combine like terms: lnx + -1lnx = 0 -5 + -2ln + -1x = -8 + -1ln + 0 + -1x -5 + -2ln + -1x = -8 + -1ln + -1x Add 'x' to each side of the equation. -5 + -2ln + -1x + x = -8 + -1ln + -1x + x Combine like terms: -1x + x = 0 -5 + -2ln + 0 = -8 + -1ln + -1x + x -5 + -2ln = -8 + -1ln + -1x + x Combine like terms: -1x + x = 0 -5 + -2ln = -8 + -1ln + 0 -5 + -2ln = -8 + -1ln Solving -5 + -2ln = -8 + -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. -5 + -2ln + ln = -8 + -1ln + ln Combine like terms: -2ln + ln = -1ln -5 + -1ln = -8 + -1ln + ln Combine like terms: -1ln + ln = 0 -5 + -1ln = -8 + 0 -5 + -1ln = -8 Add '5' to each side of the equation. -5 + 5 + -1ln = -8 + 5 Combine like terms: -5 + 5 = 0 0 + -1ln = -8 + 5 -1ln = -8 + 5 Combine like terms: -8 + 5 = -3 -1ln = -3 Divide each side by '-1n'. l = 3n-1 Simplifying l = 3n-1
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