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Simplifying ln(x2 + 7x + 12) + -1 = ln(2x2 + 9x + 4) Reorder the terms: ln(12 + 7x + x2) + -1 = ln(2x2 + 9x + 4) (12 * ln + 7x * ln + x2 * ln) + -1 = ln(2x2 + 9x + 4) (12ln + 7lnx + lnx2) + -1 = ln(2x2 + 9x + 4) Reorder the terms: -1 + 12ln + 7lnx + lnx2 = ln(2x2 + 9x + 4) Reorder the terms: -1 + 12ln + 7lnx + lnx2 = ln(4 + 9x + 2x2) -1 + 12ln + 7lnx + lnx2 = (4 * ln + 9x * ln + 2x2 * ln) -1 + 12ln + 7lnx + lnx2 = (4ln + 9lnx + 2lnx2) Solving -1 + 12ln + 7lnx + lnx2 = 4ln + 9lnx + 2lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. -1 + 12ln + 7lnx + -4ln + lnx2 = 4ln + 9lnx + -4ln + 2lnx2 Reorder the terms: -1 + 12ln + -4ln + 7lnx + lnx2 = 4ln + 9lnx + -4ln + 2lnx2 Combine like terms: 12ln + -4ln = 8ln -1 + 8ln + 7lnx + lnx2 = 4ln + 9lnx + -4ln + 2lnx2 Reorder the terms: -1 + 8ln + 7lnx + lnx2 = 4ln + -4ln + 9lnx + 2lnx2 Combine like terms: 4ln + -4ln = 0 -1 + 8ln + 7lnx + lnx2 = 0 + 9lnx + 2lnx2 -1 + 8ln + 7lnx + lnx2 = 9lnx + 2lnx2 Add '-9lnx' to each side of the equation. -1 + 8ln + 7lnx + -9lnx + lnx2 = 9lnx + -9lnx + 2lnx2 Combine like terms: 7lnx + -9lnx = -2lnx -1 + 8ln + -2lnx + lnx2 = 9lnx + -9lnx + 2lnx2 Combine like terms: 9lnx + -9lnx = 0 -1 + 8ln + -2lnx + lnx2 = 0 + 2lnx2 -1 + 8ln + -2lnx + lnx2 = 2lnx2 Add '-2lnx2' to each side of the equation. -1 + 8ln + -2lnx + lnx2 + -2lnx2 = 2lnx2 + -2lnx2 Combine like terms: lnx2 + -2lnx2 = -1lnx2 -1 + 8ln + -2lnx + -1lnx2 = 2lnx2 + -2lnx2 Combine like terms: 2lnx2 + -2lnx2 = 0 -1 + 8ln + -2lnx + -1lnx2 = 0 Add '1' to each side of the equation. -1 + 8ln + -2lnx + 1 + -1lnx2 = 0 + 1 Reorder the terms: -1 + 1 + 8ln + -2lnx + -1lnx2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8ln + -2lnx + -1lnx2 = 0 + 1 8ln + -2lnx + -1lnx2 = 0 + 1 Combine like terms: 0 + 1 = 1 8ln + -2lnx + -1lnx2 = 1 Reorder the terms: -1 + 8ln + -2lnx + -1lnx2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 8ln + -2lnx + -1lnx2 = 0 The solution to this equation could not be determined.
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