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Simplifying ln(x + 14) + -1ln(8 + -3x) = 3ln(2) Reorder the terms: ln(14 + x) + -1ln(8 + -3x) = 3ln(2) (14 * ln + x * ln) + -1ln(8 + -3x) = 3ln(2) (14ln + lnx) + -1ln(8 + -3x) = 3ln(2) 14ln + lnx + (8 * -1ln + -3x * -1ln) = 3ln(2) 14ln + lnx + (-8ln + 3lnx) = 3ln(2) Reorder the terms: 14ln + -8ln + lnx + 3lnx = 3ln(2) Combine like terms: 14ln + -8ln = 6ln 6ln + lnx + 3lnx = 3ln(2) Combine like terms: lnx + 3lnx = 4lnx 6ln + 4lnx = 3ln(2) Reorder the terms for easier multiplication: 6ln + 4lnx = 3 * 2ln Multiply 3 * 2 6ln + 4lnx = 6ln Add '-6ln' to each side of the equation. 6ln + -6ln + 4lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 0 + 4lnx = 6ln + -6ln 4lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 4lnx = 0 Solving 4lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Divide each side by '4'. lnx = 0 Simplifying lnx = 0 The solution to this equation could not be determined.
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