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Simplifying ln(15k + 2) = 2ln(k) + ln * 8 Reorder the terms: ln(2 + 15k) = 2ln(k) + ln * 8 (2 * ln + 15k * ln) = 2ln(k) + ln * 8 Reorder the terms: (15kln + 2ln) = 2ln(k) + ln * 8 (15kln + 2ln) = 2ln(k) + ln * 8 Multiply ln * k 15kln + 2ln = 2kln + ln * 8 Reorder the terms for easier multiplication: 15kln + 2ln = 2kln + 8ln Solving 15kln + 2ln = 2kln + 8ln Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2kln' to each side of the equation. 15kln + -2kln + 2ln = 2kln + -2kln + 8ln Combine like terms: 15kln + -2kln = 13kln 13kln + 2ln = 2kln + -2kln + 8ln Combine like terms: 2kln + -2kln = 0 13kln + 2ln = 0 + 8ln 13kln + 2ln = 8ln Add '-2ln' to each side of the equation. 13kln + 2ln + -2ln = 8ln + -2ln Combine like terms: 2ln + -2ln = 0 13kln + 0 = 8ln + -2ln 13kln = 8ln + -2ln Combine like terms: 8ln + -2ln = 6ln 13kln = 6ln Divide each side by '13ln'. k = 0.4615384615 Simplifying k = 0.4615384615
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