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Simplifying 2ln(2x + -1) + ln(x + -1) = ln(6x + -3) Reorder the terms: 2ln(-1 + 2x) + ln(x + -1) = ln(6x + -3) (-1 * 2ln + 2x * 2ln) + ln(x + -1) = ln(6x + -3) (-2ln + 4lnx) + ln(x + -1) = ln(6x + -3) Reorder the terms: -2ln + 4lnx + ln(-1 + x) = ln(6x + -3) -2ln + 4lnx + (-1 * ln + x * ln) = ln(6x + -3) -2ln + 4lnx + (-1ln + lnx) = ln(6x + -3) Reorder the terms: -2ln + -1ln + 4lnx + lnx = ln(6x + -3) Combine like terms: -2ln + -1ln = -3ln -3ln + 4lnx + lnx = ln(6x + -3) Combine like terms: 4lnx + lnx = 5lnx -3ln + 5lnx = ln(6x + -3) Reorder the terms: -3ln + 5lnx = ln(-3 + 6x) -3ln + 5lnx = (-3 * ln + 6x * ln) -3ln + 5lnx = (-3ln + 6lnx) Add '3ln' to each side of the equation. -3ln + 3ln + 5lnx = -3ln + 3ln + 6lnx Combine like terms: -3ln + 3ln = 0 0 + 5lnx = -3ln + 3ln + 6lnx 5lnx = -3ln + 3ln + 6lnx Combine like terms: -3ln + 3ln = 0 5lnx = 0 + 6lnx 5lnx = 6lnx Solving 5lnx = 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx' to each side of the equation. 5lnx + -6lnx = 6lnx + -6lnx Combine like terms: 5lnx + -6lnx = -1lnx -1lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -1lnx = 0 Divide each side by '-1'. lnx = 0 Simplifying lnx = 0 The solution to this equation could not be determined.
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