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Simplifying ln(x + 2.5) = 12 + -1ln(x + 1.3) Reorder the terms: ln(2.5 + x) = 12 + -1ln(x + 1.3) (2.5 * ln + x * ln) = 12 + -1ln(x + 1.3) (2.5ln + lnx) = 12 + -1ln(x + 1.3) Reorder the terms: 2.5ln + lnx = 12 + -1ln(1.3 + x) 2.5ln + lnx = 12 + (1.3 * -1ln + x * -1ln) 2.5ln + lnx = 12 + (-1.3ln + -1lnx) Solving 2.5ln + lnx = 12 + -1.3ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '1.3ln' to each side of the equation. 2.5ln + 1.3ln + lnx = 12 + -1.3ln + 1.3ln + -1lnx Combine like terms: 2.5ln + 1.3ln = 3.8ln 3.8ln + lnx = 12 + -1.3ln + 1.3ln + -1lnx Combine like terms: -1.3ln + 1.3ln = 0.0 3.8ln + lnx = 12 + 0.0 + -1lnx 3.8ln + lnx = 12 + -1lnx Add 'lnx' to each side of the equation. 3.8ln + lnx + lnx = 12 + -1lnx + lnx Combine like terms: lnx + lnx = 2lnx 3.8ln + 2lnx = 12 + -1lnx + lnx Combine like terms: -1lnx + lnx = 0 3.8ln + 2lnx = 12 + 0 3.8ln + 2lnx = 12 Reorder the terms: -12 + 3.8ln + 2lnx = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 3.8ln + 2lnx = 0 The solution to this equation could not be determined.
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