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Simplifying Ln(1 + -1x) + -1lnx = 1 (1 * nL + -1x * nL) + -1lnx = 1 (1nL + -1nxL) + -1lnx = 1 Reorder the terms: -1lnx + 1nL + -1nxL = 1 Solving -1lnx + 1nL + -1nxL = 1 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. -1lnx + 1nL + -1nL + -1nxL = 1 + -1nL Combine like terms: 1nL + -1nL = 0 -1lnx + 0 + -1nxL = 1 + -1nL -1lnx + -1nxL = 1 + -1nL Add 'nxL' to each side of the equation. -1lnx + -1nxL + nxL = 1 + -1nL + nxL Combine like terms: -1nxL + nxL = 0 -1lnx + 0 = 1 + -1nL + nxL -1lnx = 1 + -1nL + nxL Divide each side by '-1nx'. l = -1n-1x-1 + x-1L + -1L Simplifying l = -1n-1x-1 + x-1L + -1L Reorder the terms: l = -1L + -1n-1x-1 + x-1L
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