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Simplifying ln(x + 5) = ln(x + -1) + -1(x + 1) Reorder the terms: ln(5 + x) = ln(x + -1) + -1(x + 1) (5 * ln + x * ln) = ln(x + -1) + -1(x + 1) (5ln + lnx) = ln(x + -1) + -1(x + 1) Reorder the terms: 5ln + lnx = ln(-1 + x) + -1(x + 1) 5ln + lnx = (-1 * ln + x * ln) + -1(x + 1) 5ln + lnx = (-1ln + lnx) + -1(x + 1) Reorder the terms: 5ln + lnx = -1ln + lnx + -1(1 + x) 5ln + lnx = -1ln + lnx + (1 * -1 + x * -1) 5ln + lnx = -1ln + lnx + (-1 + -1x) Reorder the terms: 5ln + lnx = -1 + -1ln + lnx + -1x Add '-1lnx' to each side of the equation. 5ln + lnx + -1lnx = -1 + -1ln + lnx + -1lnx + -1x Combine like terms: lnx + -1lnx = 0 5ln + 0 = -1 + -1ln + lnx + -1lnx + -1x 5ln = -1 + -1ln + lnx + -1lnx + -1x Combine like terms: lnx + -1lnx = 0 5ln = -1 + -1ln + 0 + -1x 5ln = -1 + -1ln + -1x Solving 5ln = -1 + -1ln + -1x Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 5ln + ln = -1 + -1ln + ln + -1x Combine like terms: 5ln + ln = 6ln 6ln = -1 + -1ln + ln + -1x Combine like terms: -1ln + ln = 0 6ln = -1 + 0 + -1x 6ln = -1 + -1x Divide each side by '6n'. l = -0.1666666667n-1 + -0.1666666667n-1x Simplifying l = -0.1666666667n-1 + -0.1666666667n-1x
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