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