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Simplifying n(1 + -2y) + -1lny = 3ln(2x) + -5x (1 * n + -2y * n) + -1lny = 3ln(2x) + -5x (1n + -2ny) + -1lny = 3ln(2x) + -5x Reorder the terms: -1lny + 1n + -2ny = 3ln(2x) + -5x Remove parenthesis around (2x) -1lny + 1n + -2ny = 3ln * 2x + -5x Reorder the terms for easier multiplication: -1lny + 1n + -2ny = 3 * 2ln * x + -5x Multiply 3 * 2 -1lny + 1n + -2ny = 6ln * x + -5x Multiply ln * x -1lny + 1n + -2ny = 6lnx + -5x Solving -1lny + 1n + -2ny = 6lnx + -5x Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx' to each side of the equation. -1lny + 1n + -6lnx + -2ny = 6lnx + -6lnx + -5x Reorder the terms: -6lnx + -1lny + 1n + -2ny = 6lnx + -6lnx + -5x Combine like terms: 6lnx + -6lnx = 0 -6lnx + -1lny + 1n + -2ny = 0 + -5x -6lnx + -1lny + 1n + -2ny = -5x Add '-1n' to each side of the equation. -6lnx + -1lny + 1n + -1n + -2ny = -1n + -5x Combine like terms: 1n + -1n = 0 -6lnx + -1lny + 0 + -2ny = -1n + -5x -6lnx + -1lny + -2ny = -1n + -5x Add '2ny' to each side of the equation. -6lnx + -1lny + -2ny + 2ny = -1n + 2ny + -5x Combine like terms: -2ny + 2ny = 0 -6lnx + -1lny + 0 = -1n + 2ny + -5x -6lnx + -1lny = -1n + 2ny + -5x Reorder the terms: -6lnx + -1lny + n + -2ny + 5x = -1n + n + 2ny + -2ny + -5x + 5x Combine like terms: -1n + n = 0 -6lnx + -1lny + n + -2ny + 5x = 0 + 2ny + -2ny + -5x + 5x -6lnx + -1lny + n + -2ny + 5x = 2ny + -2ny + -5x + 5x Combine like terms: 2ny + -2ny = 0 -6lnx + -1lny + n + -2ny + 5x = 0 + -5x + 5x -6lnx + -1lny + n + -2ny + 5x = -5x + 5x Combine like terms: -5x + 5x = 0 -6lnx + -1lny + n + -2ny + 5x = 0 The solution to this equation could not be determined.
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