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