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Simplifying Ln(2y + -1) + -1ln(3 + -1y) = 1 Reorder the terms: nL(-1 + 2y) + -1ln(3 + -1y) = 1 (-1 * nL + 2y * nL) + -1ln(3 + -1y) = 1 (-1nL + 2nyL) + -1ln(3 + -1y) = 1 -1nL + 2nyL + (3 * -1ln + -1y * -1ln) = 1 -1nL + 2nyL + (-3ln + 1lny) = 1 Reorder the terms: -3ln + 1lny + -1nL + 2nyL = 1 Solving -3ln + 1lny + -1nL + 2nyL = 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. -3ln + 1lny + -1nL + nL + 2nyL = 1 + nL Combine like terms: -1nL + nL = 0 -3ln + 1lny + 0 + 2nyL = 1 + nL -3ln + 1lny + 2nyL = 1 + nL Add '-2nyL' to each side of the equation. -3ln + 1lny + 2nyL + -2nyL = 1 + nL + -2nyL Combine like terms: 2nyL + -2nyL = 0 -3ln + 1lny + 0 = 1 + nL + -2nyL -3ln + 1lny = 1 + nL + -2nyL Reorder the terms: -1 + -3ln + 1lny + -1nL + 2nyL = 1 + nL + -2nyL + -1 + -1nL + 2nyL Reorder the terms: -1 + -3ln + 1lny + -1nL + 2nyL = 1 + -1 + nL + -1nL + -2nyL + 2nyL Combine like terms: 1 + -1 = 0 -1 + -3ln + 1lny + -1nL + 2nyL = 0 + nL + -1nL + -2nyL + 2nyL -1 + -3ln + 1lny + -1nL + 2nyL = nL + -1nL + -2nyL + 2nyL Combine like terms: nL + -1nL = 0 -1 + -3ln + 1lny + -1nL + 2nyL = 0 + -2nyL + 2nyL -1 + -3ln + 1lny + -1nL + 2nyL = -2nyL + 2nyL Combine like terms: -2nyL + 2nyL = 0 -1 + -3ln + 1lny + -1nL + 2nyL = 0 The solution to this equation could not be determined.
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