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Simplifying Ln(x + -3) + -1lnx = ln(5x) Reorder the terms: nL(-3 + x) + -1lnx = ln(5x) (-3 * nL + x * nL) + -1lnx = ln(5x) (-3nL + nxL) + -1lnx = ln(5x) Reorder the terms: -1lnx + -3nL + nxL = ln(5x) Remove parenthesis around (5x) -1lnx + -3nL + nxL = ln * 5x Reorder the terms for easier multiplication: -1lnx + -3nL + nxL = 5ln * x Multiply ln * x -1lnx + -3nL + nxL = 5lnx Solving -1lnx + -3nL + nxL = 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5lnx' to each side of the equation. -1lnx + -3nL + -5lnx + nxL = 5lnx + -5lnx Reorder the terms: -1lnx + -5lnx + -3nL + nxL = 5lnx + -5lnx Combine like terms: -1lnx + -5lnx = -6lnx -6lnx + -3nL + nxL = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -6lnx + -3nL + nxL = 0 Add '3nL' to each side of the equation. -6lnx + -3nL + 3nL + nxL = 0 + 3nL Combine like terms: -3nL + 3nL = 0 -6lnx + 0 + nxL = 0 + 3nL -6lnx + nxL = 0 + 3nL Remove the zero: -6lnx + nxL = 3nL Add '-1nxL' to each side of the equation. -6lnx + nxL + -1nxL = 3nL + -1nxL Combine like terms: nxL + -1nxL = 0 -6lnx + 0 = 3nL + -1nxL -6lnx = 3nL + -1nxL Divide each side by '-6nx'. l = -0.5x-1L + 0.1666666667L Simplifying l = -0.5x-1L + 0.1666666667L Reorder the terms: l = 0.1666666667L + -0.5x-1L
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