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Simplifying lnx + -1 = ln(5) + ln(x + -2) Reorder the terms: -1 + lnx = ln(5) + ln(x + -2) Reorder the terms for easier multiplication: -1 + lnx = 5ln + ln(x + -2) Reorder the terms: -1 + lnx = 5ln + ln(-2 + x) -1 + lnx = 5ln + (-2 * ln + x * ln) -1 + lnx = 5ln + (-2ln + lnx) Combine like terms: 5ln + -2ln = 3ln -1 + lnx = 3ln + lnx Add '-1lnx' to each side of the equation. -1 + lnx + -1lnx = 3ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -1 + 0 = 3ln + lnx + -1lnx -1 = 3ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -1 = 3ln + 0 -1 = 3ln Solving -1 = 3ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. -1 + -3ln = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 -1 + -3ln = 0 Add '1' to each side of the equation. -1 + 1 + -3ln = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3ln = 0 + 1 -3ln = 0 + 1 Combine like terms: 0 + 1 = 1 -3ln = 1 Divide each side by '-3n'. l = -0.3333333333n-1 Simplifying l = -0.3333333333n-1
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