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Simplifying ln(2x + 14) + -1ln(x + 2) = ln(x + -5) Reorder the terms: ln(14 + 2x) + -1ln(x + 2) = ln(x + -5) (14 * ln + 2x * ln) + -1ln(x + 2) = ln(x + -5) (14ln + 2lnx) + -1ln(x + 2) = ln(x + -5) Reorder the terms: 14ln + 2lnx + -1ln(2 + x) = ln(x + -5) 14ln + 2lnx + (2 * -1ln + x * -1ln) = ln(x + -5) 14ln + 2lnx + (-2ln + -1lnx) = ln(x + -5) Reorder the terms: 14ln + -2ln + 2lnx + -1lnx = ln(x + -5) Combine like terms: 14ln + -2ln = 12ln 12ln + 2lnx + -1lnx = ln(x + -5) Combine like terms: 2lnx + -1lnx = 1lnx 12ln + 1lnx = ln(x + -5) Reorder the terms: 12ln + 1lnx = ln(-5 + x) 12ln + 1lnx = (-5 * ln + x * ln) 12ln + 1lnx = (-5ln + lnx) Solving 12ln + 1lnx = -5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 12ln + 5ln + 1lnx = -5ln + 5ln + lnx Combine like terms: 12ln + 5ln = 17ln 17ln + 1lnx = -5ln + 5ln + lnx Combine like terms: -5ln + 5ln = 0 17ln + 1lnx = 0 + lnx 17ln + 1lnx = lnx Add '-1lnx' to each side of the equation. 17ln + 1lnx + -1lnx = lnx + -1lnx Combine like terms: 1lnx + -1lnx = 0 17ln + 0 = lnx + -1lnx 17ln = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 17ln = 0 Divide each side by '17'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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