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