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Simplifying 0 = 8 + 4ln(4) + -1(0.5 + 4ln(1)) Reorder the terms for easier multiplication: 0 = 8 + 4 * 4ln + -1(0.5 + 4ln(1)) Multiply 4 * 4 0 = 8 + 16ln + -1(0.5 + 4ln(1)) Reorder the terms for easier multiplication: 0 = 8 + 16ln + -1(0.5 + 4 * 1ln) Multiply 4 * 1 0 = 8 + 16ln + -1(0.5 + 4ln) 0 = 8 + 16ln + (0.5 * -1 + 4ln * -1) 0 = 8 + 16ln + (-0.5 + -4ln) Reorder the terms: 0 = 8 + -0.5 + 16ln + -4ln Combine like terms: 8 + -0.5 = 7.5 0 = 7.5 + 16ln + -4ln Combine like terms: 16ln + -4ln = 12ln 0 = 7.5 + 12ln Solving 0 = 7.5 + 12ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 0 + -12ln = 7.5 + 12ln + -12ln Remove the zero: -12ln = 7.5 + 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -12ln = 7.5 + 0 -12ln = 7.5 Divide each side by '-12n'. l = -0.625n-1 Simplifying l = -0.625n-1
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