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Simplifying ln(x + 3) + ln(x + -2) = ln(2x + 24) Reorder the terms: ln(3 + x) + ln(x + -2) = ln(2x + 24) (3 * ln + x * ln) + ln(x + -2) = ln(2x + 24) (3ln + lnx) + ln(x + -2) = ln(2x + 24) Reorder the terms: 3ln + lnx + ln(-2 + x) = ln(2x + 24) 3ln + lnx + (-2 * ln + x * ln) = ln(2x + 24) 3ln + lnx + (-2ln + lnx) = ln(2x + 24) Reorder the terms: 3ln + -2ln + lnx + lnx = ln(2x + 24) Combine like terms: 3ln + -2ln = 1ln 1ln + lnx + lnx = ln(2x + 24) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(2x + 24) Reorder the terms: 1ln + 2lnx = ln(24 + 2x) 1ln + 2lnx = (24 * ln + 2x * ln) 1ln + 2lnx = (24ln + 2lnx) Add '-2lnx' to each side of the equation. 1ln + 2lnx + -2lnx = 24ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 1ln + 0 = 24ln + 2lnx + -2lnx 1ln = 24ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 1ln = 24ln + 0 1ln = 24ln Solving 1ln = 24ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. 1ln + -24ln = 24ln + -24ln Combine like terms: 1ln + -24ln = -23ln -23ln = 24ln + -24ln Combine like terms: 24ln + -24ln = 0 -23ln = 0 Divide each side by '-23'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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