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Simplifying ln(3 + -1x) + ln(-2 + -1x) = ln(1 + -7x) (3 * ln + -1x * ln) + ln(-2 + -1x) = ln(1 + -7x) (3ln + -1lnx) + ln(-2 + -1x) = ln(1 + -7x) 3ln + -1lnx + (-2 * ln + -1x * ln) = ln(1 + -7x) 3ln + -1lnx + (-2ln + -1lnx) = ln(1 + -7x) Reorder the terms: 3ln + -2ln + -1lnx + -1lnx = ln(1 + -7x) Combine like terms: 3ln + -2ln = 1ln 1ln + -1lnx + -1lnx = ln(1 + -7x) Combine like terms: -1lnx + -1lnx = -2lnx 1ln + -2lnx = ln(1 + -7x) 1ln + -2lnx = (1 * ln + -7x * ln) 1ln + -2lnx = (1ln + -7lnx) Add '-1ln' to each side of the equation. 1ln + -1ln + -2lnx = 1ln + -1ln + -7lnx Combine like terms: 1ln + -1ln = 0 0 + -2lnx = 1ln + -1ln + -7lnx -2lnx = 1ln + -1ln + -7lnx Combine like terms: 1ln + -1ln = 0 -2lnx = 0 + -7lnx -2lnx = -7lnx Solving -2lnx = -7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '7lnx' to each side of the equation. -2lnx + 7lnx = -7lnx + 7lnx Combine like terms: -2lnx + 7lnx = 5lnx 5lnx = -7lnx + 7lnx Combine like terms: -7lnx + 7lnx = 0 5lnx = 0 Divide each side by '5'. lnx = 0 Simplifying lnx = 0 The solution to this equation could not be determined.
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