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Simplifying ln(1 + -4k) = 8k (1 * ln + -4k * ln) = 8k Reorder the terms: (-4kln + 1ln) = 8k (-4kln + 1ln) = 8k Solving -4kln + 1ln = 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. -4kln + -8k + 1ln = 8k + -8k Reorder the terms: -8k + -4kln + 1ln = 8k + -8k Combine like terms: 8k + -8k = 0 -8k + -4kln + 1ln = 0 Add '-1ln' to each side of the equation. -8k + -4kln + 1ln + -1ln = 0 + -1ln Combine like terms: 1ln + -1ln = 0 -8k + -4kln + 0 = 0 + -1ln -8k + -4kln = 0 + -1ln Remove the zero: -8k + -4kln = -1ln Combine like terms: -1ln + ln = 0 -8k + -4kln + ln = 0 The solution to this equation could not be determined.
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