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Simplifying ln(3x + -9) + kn(9) = 1 Reorder the terms: ln(-9 + 3x) + kn(9) = 1 (-9 * ln + 3x * ln) + kn(9) = 1 (-9ln + 3lnx) + kn(9) = 1 Reorder the terms for easier multiplication: -9ln + 3lnx + 9kn = 1 Reorder the terms: 9kn + -9ln + 3lnx = 1 Solving 9kn + -9ln + 3lnx = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9ln' to each side of the equation. 9kn + -9ln + 9ln + 3lnx = 1 + 9ln Combine like terms: -9ln + 9ln = 0 9kn + 0 + 3lnx = 1 + 9ln 9kn + 3lnx = 1 + 9ln Add '-3lnx' to each side of the equation. 9kn + 3lnx + -3lnx = 1 + 9ln + -3lnx Combine like terms: 3lnx + -3lnx = 0 9kn + 0 = 1 + 9ln + -3lnx 9kn = 1 + 9ln + -3lnx Divide each side by '9n'. k = 0.1111111111n-1 + l + -0.3333333333lx Simplifying k = 0.1111111111n-1 + l + -0.3333333333lx Reorder the terms: k = l + -0.3333333333lx + 0.1111111111n-1
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