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Simplifying 0 = ln(x) + -1ln(1 + -1x) + 3.9(1 + -2x) Multiply ln * x 0 = lnx + -1ln(1 + -1x) + 3.9(1 + -2x) 0 = lnx + (1 * -1ln + -1x * -1ln) + 3.9(1 + -2x) 0 = lnx + (-1ln + 1lnx) + 3.9(1 + -2x) 0 = lnx + -1ln + 1lnx + (1 * 3.9 + -2x * 3.9) 0 = lnx + -1ln + 1lnx + (3.9 + -7.8x) Reorder the terms: 0 = 3.9 + -1ln + lnx + 1lnx + -7.8x Combine like terms: lnx + 1lnx = 2lnx 0 = 3.9 + -1ln + 2lnx + -7.8x Solving 0 = 3.9 + -1ln + 2lnx + -7.8x Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 0 + ln = 3.9 + -1ln + 2lnx + ln + -7.8x Remove the zero: ln = 3.9 + -1ln + 2lnx + ln + -7.8x Reorder the terms: ln = 3.9 + -1ln + ln + 2lnx + -7.8x Combine like terms: -1ln + ln = 0 ln = 3.9 + 0 + 2lnx + -7.8x ln = 3.9 + 2lnx + -7.8x Add '-2lnx' to each side of the equation. ln + -2lnx = 3.9 + 2lnx + -2lnx + -7.8x Combine like terms: 2lnx + -2lnx = 0 ln + -2lnx = 3.9 + 0 + -7.8x ln + -2lnx = 3.9 + -7.8x Reorder the terms: -3.9 + ln + -2lnx + 7.8x = 3.9 + -7.8x + -3.9 + 7.8x Reorder the terms: -3.9 + ln + -2lnx + 7.8x = 3.9 + -3.9 + -7.8x + 7.8x Combine like terms: 3.9 + -3.9 = 0.0 -3.9 + ln + -2lnx + 7.8x = 0.0 + -7.8x + 7.8x -3.9 + ln + -2lnx + 7.8x = -7.8x + 7.8x Combine like terms: -7.8x + 7.8x = 0.0 -3.9 + ln + -2lnx + 7.8x = 0.0 The solution to this equation could not be determined.
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