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Simplifying (x + -1) + ln(x + 2) = ln(6x + -8) Reorder the terms: (-1 + x) + ln(x + 2) = ln(6x + -8) Remove parenthesis around (-1 + x) -1 + x + ln(x + 2) = ln(6x + -8) Reorder the terms: -1 + x + ln(2 + x) = ln(6x + -8) -1 + x + (2 * ln + x * ln) = ln(6x + -8) -1 + x + (2ln + lnx) = ln(6x + -8) Reorder the terms: -1 + 2ln + lnx + x = ln(6x + -8) Reorder the terms: -1 + 2ln + lnx + x = ln(-8 + 6x) -1 + 2ln + lnx + x = (-8 * ln + 6x * ln) -1 + 2ln + lnx + x = (-8ln + 6lnx) Solving -1 + 2ln + lnx + x = -8ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8ln' to each side of the equation. -1 + 2ln + lnx + 8ln + x = -8ln + 8ln + 6lnx Reorder the terms: -1 + 2ln + 8ln + lnx + x = -8ln + 8ln + 6lnx Combine like terms: 2ln + 8ln = 10ln -1 + 10ln + lnx + x = -8ln + 8ln + 6lnx Combine like terms: -8ln + 8ln = 0 -1 + 10ln + lnx + x = 0 + 6lnx -1 + 10ln + lnx + x = 6lnx Add '-6lnx' to each side of the equation. -1 + 10ln + lnx + -6lnx + x = 6lnx + -6lnx Combine like terms: lnx + -6lnx = -5lnx -1 + 10ln + -5lnx + x = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -1 + 10ln + -5lnx + x = 0 Add '1' to each side of the equation. -1 + 10ln + -5lnx + 1 + x = 0 + 1 Reorder the terms: -1 + 1 + 10ln + -5lnx + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 10ln + -5lnx + x = 0 + 1 10ln + -5lnx + x = 0 + 1 Combine like terms: 0 + 1 = 1 10ln + -5lnx + x = 1 Add '-1x' to each side of the equation. 10ln + -5lnx + x + -1x = 1 + -1x Combine like terms: x + -1x = 0 10ln + -5lnx + 0 = 1 + -1x 10ln + -5lnx = 1 + -1x Reorder the terms: -1 + 10ln + -5lnx + x = 1 + -1x + -1 + x Reorder the terms: -1 + 10ln + -5lnx + x = 1 + -1 + -1x + x Combine like terms: 1 + -1 = 0 -1 + 10ln + -5lnx + x = 0 + -1x + x -1 + 10ln + -5lnx + x = -1x + x Combine like terms: -1x + x = 0 -1 + 10ln + -5lnx + x = 0 The solution to this equation could not be determined.
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