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Simplifying Ln(x + -1) + Ln(x + -2) = Ln(2x + 1) Reorder the terms: nL(-1 + x) + Ln(x + -2) = Ln(2x + 1) (-1 * nL + x * nL) + Ln(x + -2) = Ln(2x + 1) (-1nL + nxL) + Ln(x + -2) = Ln(2x + 1) Reorder the terms: -1nL + nxL + nL(-2 + x) = Ln(2x + 1) -1nL + nxL + (-2 * nL + x * nL) = Ln(2x + 1) -1nL + nxL + (-2nL + nxL) = Ln(2x + 1) Reorder the terms: -1nL + -2nL + nxL + nxL = Ln(2x + 1) Combine like terms: -1nL + -2nL = -3nL -3nL + nxL + nxL = Ln(2x + 1) Combine like terms: nxL + nxL = 2nxL -3nL + 2nxL = Ln(2x + 1) Reorder the terms: -3nL + 2nxL = nL(1 + 2x) -3nL + 2nxL = (1 * nL + 2x * nL) -3nL + 2nxL = (1nL + 2nxL) Add '-2nxL' to each side of the equation. -3nL + 2nxL + -2nxL = 1nL + 2nxL + -2nxL Combine like terms: 2nxL + -2nxL = 0 -3nL + 0 = 1nL + 2nxL + -2nxL -3nL = 1nL + 2nxL + -2nxL Combine like terms: 2nxL + -2nxL = 0 -3nL = 1nL + 0 -3nL = 1nL Solving -3nL = 1nL 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. -3nL + -1nL = 1nL + -1nL Combine like terms: -3nL + -1nL = -4nL -4nL = 1nL + -1nL Combine like terms: 1nL + -1nL = 0 -4nL = 0 Divide each side by '-4'. nL = 0 Simplifying nL = 0 The solution to this equation could not be determined.
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