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Simplifying ln(7x + 1) = ln(x + -2) + 1 Reorder the terms: ln(1 + 7x) = ln(x + -2) + 1 (1 * ln + 7x * ln) = ln(x + -2) + 1 (1ln + 7lnx) = ln(x + -2) + 1 Reorder the terms: 1ln + 7lnx = ln(-2 + x) + 1 1ln + 7lnx = (-2 * ln + x * ln) + 1 1ln + 7lnx = (-2ln + lnx) + 1 Reorder the terms: 1ln + 7lnx = 1 + -2ln + lnx Solving 1ln + 7lnx = 1 + -2ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 1ln + 2ln + 7lnx = 1 + -2ln + 2ln + lnx Combine like terms: 1ln + 2ln = 3ln 3ln + 7lnx = 1 + -2ln + 2ln + lnx Combine like terms: -2ln + 2ln = 0 3ln + 7lnx = 1 + 0 + lnx 3ln + 7lnx = 1 + lnx Add '-1lnx' to each side of the equation. 3ln + 7lnx + -1lnx = 1 + lnx + -1lnx Combine like terms: 7lnx + -1lnx = 6lnx 3ln + 6lnx = 1 + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 3ln + 6lnx = 1 + 0 3ln + 6lnx = 1 Reorder the terms: -1 + 3ln + 6lnx = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 3ln + 6lnx = 0 The solution to this equation could not be determined.
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