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