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Simplifying 0 = 2.5 + -5x + -1ln(1 + -1x) + ln(x) 0 = 2.5 + -5x + (1 * -1ln + -1x * -1ln) + ln(x) 0 = 2.5 + -5x + (-1ln + 1lnx) + ln(x) Multiply ln * x 0 = 2.5 + -5x + -1ln + 1lnx + lnx Reorder the terms: 0 = 2.5 + -1ln + 1lnx + lnx + -5x Combine like terms: 1lnx + lnx = 2lnx 0 = 2.5 + -1ln + 2lnx + -5x Solving 0 = 2.5 + -1ln + 2lnx + -5x 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 = 2.5 + -1ln + 2lnx + ln + -5x Remove the zero: ln = 2.5 + -1ln + 2lnx + ln + -5x Reorder the terms: ln = 2.5 + -1ln + ln + 2lnx + -5x Combine like terms: -1ln + ln = 0 ln = 2.5 + 0 + 2lnx + -5x ln = 2.5 + 2lnx + -5x Add '-2lnx' to each side of the equation. ln + -2lnx = 2.5 + 2lnx + -2lnx + -5x Combine like terms: 2lnx + -2lnx = 0 ln + -2lnx = 2.5 + 0 + -5x ln + -2lnx = 2.5 + -5x Reorder the terms: -2.5 + ln + -2lnx + 5x = 2.5 + -5x + -2.5 + 5x Reorder the terms: -2.5 + ln + -2lnx + 5x = 2.5 + -2.5 + -5x + 5x Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + ln + -2lnx + 5x = 0.0 + -5x + 5x -2.5 + ln + -2lnx + 5x = -5x + 5x Combine like terms: -5x + 5x = 0 -2.5 + ln + -2lnx + 5x = 0 The solution to this equation could not be determined.
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