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Simplifying ln(x + 3) + -4 = ln(x + -5) Reorder the terms: ln(3 + x) + -4 = ln(x + -5) (3 * ln + x * ln) + -4 = ln(x + -5) (3ln + lnx) + -4 = ln(x + -5) Reorder the terms: -4 + 3ln + lnx = ln(x + -5) Reorder the terms: -4 + 3ln + lnx = ln(-5 + x) -4 + 3ln + lnx = (-5 * ln + x * ln) -4 + 3ln + lnx = (-5ln + lnx) Add '-1lnx' to each side of the equation. -4 + 3ln + lnx + -1lnx = -5ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -4 + 3ln + 0 = -5ln + lnx + -1lnx -4 + 3ln = -5ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -4 + 3ln = -5ln + 0 -4 + 3ln = -5ln Solving -4 + 3ln = -5ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. -4 + 3ln + 5ln = -5ln + 5ln Combine like terms: 3ln + 5ln = 8ln -4 + 8ln = -5ln + 5ln Combine like terms: -5ln + 5ln = 0 -4 + 8ln = 0 Add '4' to each side of the equation. -4 + 4 + 8ln = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 8ln = 0 + 4 8ln = 0 + 4 Combine like terms: 0 + 4 = 4 8ln = 4 Divide each side by '8n'. l = 0.5n-1 Simplifying l = 0.5n-1
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