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Simplifying Ln(2x + 5) + Ln(x + -4) + -2lnx = 0 Reorder the terms: nL(5 + 2x) + Ln(x + -4) + -2lnx = 0 (5 * nL + 2x * nL) + Ln(x + -4) + -2lnx = 0 (5nL + 2nxL) + Ln(x + -4) + -2lnx = 0 Reorder the terms: 5nL + 2nxL + nL(-4 + x) + -2lnx = 0 5nL + 2nxL + (-4 * nL + x * nL) + -2lnx = 0 5nL + 2nxL + (-4nL + nxL) + -2lnx = 0 Reorder the terms: -2lnx + 5nL + -4nL + 2nxL + nxL = 0 Combine like terms: 5nL + -4nL = 1nL -2lnx + 1nL + 2nxL + nxL = 0 Combine like terms: 2nxL + nxL = 3nxL -2lnx + 1nL + 3nxL = 0 Solving -2lnx + 1nL + 3nxL = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1nL' to each side of the equation. -2lnx + 1nL + -1nL + 3nxL = 0 + -1nL Combine like terms: 1nL + -1nL = 0 -2lnx + 0 + 3nxL = 0 + -1nL -2lnx + 3nxL = 0 + -1nL Remove the zero: -2lnx + 3nxL = -1nL Add '-3nxL' to each side of the equation. -2lnx + 3nxL + -3nxL = -1nL + -3nxL Combine like terms: 3nxL + -3nxL = 0 -2lnx + 0 = -1nL + -3nxL -2lnx = -1nL + -3nxL Divide each side by '-2nx'. l = 0.5x-1L + 1.5L Simplifying l = 0.5x-1L + 1.5L Reorder the terms: l = 1.5L + 0.5x-1L
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