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Simplifying 3Ln(x + 2) + -2Ln(x + 3) = Ln(x + 1) Reorder the terms: 3nL(2 + x) + -2Ln(x + 3) = Ln(x + 1) (2 * 3nL + x * 3nL) + -2Ln(x + 3) = Ln(x + 1) (6nL + 3nxL) + -2Ln(x + 3) = Ln(x + 1) Reorder the terms: 6nL + 3nxL + -2nL(3 + x) = Ln(x + 1) 6nL + 3nxL + (3 * -2nL + x * -2nL) = Ln(x + 1) 6nL + 3nxL + (-6nL + -2nxL) = Ln(x + 1) Reorder the terms: 6nL + -6nL + 3nxL + -2nxL = Ln(x + 1) Combine like terms: 6nL + -6nL = 0 0 + 3nxL + -2nxL = Ln(x + 1) 3nxL + -2nxL = Ln(x + 1) Combine like terms: 3nxL + -2nxL = 1nxL 1nxL = Ln(x + 1) Reorder the terms: 1nxL = nL(1 + x) 1nxL = (1 * nL + x * nL) 1nxL = (1nL + nxL) Solving 1nxL = 1nL + nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1nL' to each side of the equation. -1nL + 1nxL = 1nL + -1nL + nxL Combine like terms: 1nL + -1nL = 0 -1nL + 1nxL = 0 + nxL -1nL + 1nxL = nxL Add '-1nxL' to each side of the equation. -1nL + 1nxL + -1nxL = nxL + -1nxL Combine like terms: 1nxL + -1nxL = 0 -1nL + 0 = nxL + -1nxL -1nL = nxL + -1nxL Combine like terms: nxL + -1nxL = 0 -1nL = 0 Divide each side by '-1'. nL = 0 Simplifying nL = 0 The solution to this equation could not be determined.
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