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Simplifying ln(x3 + 8) + -1ln(x + 2) + -2ln(x2 + -2x + 4) = 0 Reorder the terms: ln(8 + x3) + -1ln(x + 2) + -2ln(x2 + -2x + 4) = 0 (8 * ln + x3 * ln) + -1ln(x + 2) + -2ln(x2 + -2x + 4) = 0 (8ln + lnx3) + -1ln(x + 2) + -2ln(x2 + -2x + 4) = 0 Reorder the terms: 8ln + lnx3 + -1ln(2 + x) + -2ln(x2 + -2x + 4) = 0 8ln + lnx3 + (2 * -1ln + x * -1ln) + -2ln(x2 + -2x + 4) = 0 8ln + lnx3 + (-2ln + -1lnx) + -2ln(x2 + -2x + 4) = 0 Reorder the terms: 8ln + lnx3 + -2ln + -1lnx + -2ln(4 + -2x + x2) = 0 8ln + lnx3 + -2ln + -1lnx + (4 * -2ln + -2x * -2ln + x2 * -2ln) = 0 8ln + lnx3 + -2ln + -1lnx + (-8ln + 4lnx + -2lnx2) = 0 Reorder the terms: 8ln + -2ln + -8ln + -1lnx + 4lnx + -2lnx2 + lnx3 = 0 Combine like terms: 8ln + -2ln = 6ln 6ln + -8ln + -1lnx + 4lnx + -2lnx2 + lnx3 = 0 Combine like terms: 6ln + -8ln = -2ln -2ln + -1lnx + 4lnx + -2lnx2 + lnx3 = 0 Combine like terms: -1lnx + 4lnx = 3lnx -2ln + 3lnx + -2lnx2 + lnx3 = 0 Solving -2ln + 3lnx + -2lnx2 + lnx3 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + 3x + -2x2 + x3) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-2 + 3x + -2x2 + x3)' equal to zero and attempt to solve: Simplifying -2 + 3x + -2x2 + x3 = 0 Solving -2 + 3x + -2x2 + x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 3x + -2x2 + 2 + x3 = 0 + 2 Reorder the terms: -2 + 2 + 3x + -2x2 + x3 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x + -2x2 + x3 = 0 + 2 3x + -2x2 + x3 = 0 + 2 Combine like terms: 0 + 2 = 2 3x + -2x2 + x3 = 2 Add '-3x' to each side of the equation. 3x + -2x2 + -3x + x3 = 2 + -3x Reorder the terms: 3x + -3x + -2x2 + x3 = 2 + -3x Combine like terms: 3x + -3x = 0 0 + -2x2 + x3 = 2 + -3x -2x2 + x3 = 2 + -3x Add '2x2' to each side of the equation. -2x2 + 2x2 + x3 = 2 + -3x + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + x3 = 2 + -3x + 2x2 x3 = 2 + -3x + 2x2 Add '-1x3' to each side of the equation. x3 + -1x3 = 2 + -3x + 2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = 2 + -3x + 2x2 + -1x3 Simplifying 0 = 2 + -3x + 2x2 + -1x3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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