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Simplifying ln(x2 + -4e2) = 1 + ln(3x) Reorder the terms: ln(-4e2 + x2) = 1 + ln(3x) (-4e2 * ln + x2 * ln) = 1 + ln(3x) (-4e2ln + lnx2) = 1 + ln(3x) Remove parenthesis around (3x) -4e2ln + lnx2 = 1 + ln * 3x Reorder the terms for easier multiplication: -4e2ln + lnx2 = 1 + 3ln * x Multiply ln * x -4e2ln + lnx2 = 1 + 3lnx Solving -4e2ln + lnx2 = 1 + 3lnx Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-1lnx2' to each side of the equation. -4e2ln + lnx2 + -1lnx2 = 1 + 3lnx + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -4e2ln + 0 = 1 + 3lnx + -1lnx2 -4e2ln = 1 + 3lnx + -1lnx2 Divide each side by '-4ln'. e2 = -0.25l-1n-1 + -0.75x + 0.25x2 Simplifying e2 = -0.25l-1n-1 + -0.75x + 0.25x2 Reorder the terms: e2 + 0.25l-1n-1 + 0.75x + -0.25x2 = -0.25l-1n-1 + 0.25l-1n-1 + -0.75x + 0.75x + 0.25x2 + -0.25x2 Combine like terms: -0.25l-1n-1 + 0.25l-1n-1 = 0.00 e2 + 0.25l-1n-1 + 0.75x + -0.25x2 = 0.00 + -0.75x + 0.75x + 0.25x2 + -0.25x2 e2 + 0.25l-1n-1 + 0.75x + -0.25x2 = -0.75x + 0.75x + 0.25x2 + -0.25x2 Combine like terms: -0.75x + 0.75x = 0.00 e2 + 0.25l-1n-1 + 0.75x + -0.25x2 = 0.00 + 0.25x2 + -0.25x2 e2 + 0.25l-1n-1 + 0.75x + -0.25x2 = 0.25x2 + -0.25x2 Combine like terms: 0.25x2 + -0.25x2 = 0.00 e2 + 0.25l-1n-1 + 0.75x + -0.25x2 = 0.00 The solution to this equation could not be determined.
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