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Simplifying x * ln(x + 2) + -4ln(x + 2) = 0 Reorder the terms: x * ln(2 + x) + -4ln(x + 2) = 0 Multiply x * ln lnx(2 + x) + -4ln(x + 2) = 0 (2 * lnx + x * lnx) + -4ln(x + 2) = 0 (2lnx + lnx2) + -4ln(x + 2) = 0 Reorder the terms: 2lnx + lnx2 + -4ln(2 + x) = 0 2lnx + lnx2 + (2 * -4ln + x * -4ln) = 0 2lnx + lnx2 + (-8ln + -4lnx) = 0 Reorder the terms: -8ln + 2lnx + -4lnx + lnx2 = 0 Combine like terms: 2lnx + -4lnx = -2lnx -8ln + -2lnx + lnx2 = 0 Solving -8ln + -2lnx + lnx2 = 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(-8 + -2x + x2) = 0 Factor a trinomial. ln((-2 + -1x)(4 + -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 '(-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.Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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