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Simplifying ln(9x2 + -3x + e + -1) = 1 Reorder the terms: ln(-1 + e + -3x + 9x2) = 1 (-1 * ln + e * ln + -3x * ln + 9x2 * ln) = 1 Reorder the terms: (eln + -1ln + -3lnx + 9lnx2) = 1 (eln + -1ln + -3lnx + 9lnx2) = 1 Solving eln + -1ln + -3lnx + 9lnx2 = 1 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add 'ln' to each side of the equation. eln + -1ln + -3lnx + ln + 9lnx2 = 1 + ln Reorder the terms: eln + -1ln + ln + -3lnx + 9lnx2 = 1 + ln Combine like terms: -1ln + ln = 0 eln + 0 + -3lnx + 9lnx2 = 1 + ln eln + -3lnx + 9lnx2 = 1 + ln Add '3lnx' to each side of the equation. eln + -3lnx + 3lnx + 9lnx2 = 1 + ln + 3lnx Combine like terms: -3lnx + 3lnx = 0 eln + 0 + 9lnx2 = 1 + ln + 3lnx eln + 9lnx2 = 1 + ln + 3lnx Add '-9lnx2' to each side of the equation. eln + 9lnx2 + -9lnx2 = 1 + ln + 3lnx + -9lnx2 Combine like terms: 9lnx2 + -9lnx2 = 0 eln + 0 = 1 + ln + 3lnx + -9lnx2 eln = 1 + ln + 3lnx + -9lnx2 Divide each side by 'ln'. e = l-1n-1 + 1 + 3x + -9x2 Simplifying e = l-1n-1 + 1 + 3x + -9x2 Reorder the terms: e = 1 + l-1n-1 + 3x + -9x2
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