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Simplifying 3ln(x + 8) = ln(3x) + 12.18 Reorder the terms: 3ln(8 + x) = ln(3x) + 12.18 (8 * 3ln + x * 3ln) = ln(3x) + 12.18 (24ln + 3lnx) = ln(3x) + 12.18 Remove parenthesis around (3x) 24ln + 3lnx = ln * 3x + 12.18 Reorder the terms for easier multiplication: 24ln + 3lnx = 3ln * x + 12.18 Multiply ln * x 24ln + 3lnx = 3lnx + 12.18 Reorder the terms: 24ln + 3lnx = 12.18 + 3lnx Add '-3lnx' to each side of the equation. 24ln + 3lnx + -3lnx = 12.18 + 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 24ln + 0 = 12.18 + 3lnx + -3lnx 24ln = 12.18 + 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 24ln = 12.18 + 0 24ln = 12.18 Solving 24ln = 12.18 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Divide each side by '24n'. l = 0.5075n-1 Simplifying l = 0.5075n-1
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