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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 = -5ln -5ln + lnx + lnx = ln(2x + 24) Combine like terms: lnx + lnx = 2lnx -5ln + 2lnx = ln(2x + 24) Reorder the terms: -5ln + 2lnx = ln(24 + 2x) -5ln + 2lnx = (24 * ln + 2x * ln) -5ln + 2lnx = (24ln + 2lnx) Add '-2lnx' to each side of the equation. -5ln + 2lnx + -2lnx = 24ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -5ln + 0 = 24ln + 2lnx + -2lnx -5ln = 24ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -5ln = 24ln + 0 -5ln = 24ln Solving -5ln = 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. -5ln + -24ln = 24ln + -24ln Combine like terms: -5ln + -24ln = -29ln -29ln = 24ln + -24ln Combine like terms: 24ln + -24ln = 0 -29ln = 0 Divide each side by '-29'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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