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Simplifying ln(x + 5) + ln(-1x + 10) = ln(54) Reorder the terms: ln(5 + x) + ln(-1x + 10) = ln(54) (5 * ln + x * ln) + ln(-1x + 10) = ln(54) (5ln + lnx) + ln(-1x + 10) = ln(54) Reorder the terms: 5ln + lnx + ln(10 + -1x) = ln(54) 5ln + lnx + (10 * ln + -1x * ln) = ln(54) 5ln + lnx + (10ln + -1lnx) = ln(54) Reorder the terms: 5ln + 10ln + lnx + -1lnx = ln(54) Combine like terms: 5ln + 10ln = 15ln 15ln + lnx + -1lnx = ln(54) Combine like terms: lnx + -1lnx = 0 15ln + 0 = ln(54) 15ln = ln(54) Reorder the terms for easier multiplication: 15ln = 54ln Solving 15ln = 54ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-54ln' to each side of the equation. 15ln + -54ln = 54ln + -54ln Combine like terms: 15ln + -54ln = -39ln -39ln = 54ln + -54ln Combine like terms: 54ln + -54ln = 0 -39ln = 0 Divide each side by '-39'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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