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Simplifying ln(5 + -1x) + ln(-4 + -1x) = ln(1 + -5x) (5 * ln + -1x * ln) + ln(-4 + -1x) = ln(1 + -5x) (5ln + -1lnx) + ln(-4 + -1x) = ln(1 + -5x) 5ln + -1lnx + (-4 * ln + -1x * ln) = ln(1 + -5x) 5ln + -1lnx + (-4ln + -1lnx) = ln(1 + -5x) Reorder the terms: 5ln + -4ln + -1lnx + -1lnx = ln(1 + -5x) Combine like terms: 5ln + -4ln = 1ln 1ln + -1lnx + -1lnx = ln(1 + -5x) Combine like terms: -1lnx + -1lnx = -2lnx 1ln + -2lnx = ln(1 + -5x) 1ln + -2lnx = (1 * ln + -5x * ln) 1ln + -2lnx = (1ln + -5lnx) Add '-1ln' to each side of the equation. 1ln + -1ln + -2lnx = 1ln + -1ln + -5lnx Combine like terms: 1ln + -1ln = 0 0 + -2lnx = 1ln + -1ln + -5lnx -2lnx = 1ln + -1ln + -5lnx Combine like terms: 1ln + -1ln = 0 -2lnx = 0 + -5lnx -2lnx = -5lnx Solving -2lnx = -5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5lnx' to each side of the equation. -2lnx + 5lnx = -5lnx + 5lnx Combine like terms: -2lnx + 5lnx = 3lnx 3lnx = -5lnx + 5lnx Combine like terms: -5lnx + 5lnx = 0 3lnx = 0 Divide each side by '3'. lnx = 0 Simplifying lnx = 0 The solution to this equation could not be determined.
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