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Simplifying ln(x2 + 6x + 8) + -1ln(x + 4) = 0 Reorder the terms: ln(8 + 6x + x2) + -1ln(x + 4) = 0 (8 * ln + 6x * ln + x2 * ln) + -1ln(x + 4) = 0 (8ln + 6lnx + lnx2) + -1ln(x + 4) = 0 Reorder the terms: 8ln + 6lnx + lnx2 + -1ln(4 + x) = 0 8ln + 6lnx + lnx2 + (4 * -1ln + x * -1ln) = 0 8ln + 6lnx + lnx2 + (-4ln + -1lnx) = 0 Reorder the terms: 8ln + -4ln + 6lnx + -1lnx + lnx2 = 0 Combine like terms: 8ln + -4ln = 4ln 4ln + 6lnx + -1lnx + lnx2 = 0 Combine like terms: 6lnx + -1lnx = 5lnx 4ln + 5lnx + lnx2 = 0 Solving 4ln + 5lnx + 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(4 + 5x + x2) = 0 Factor a trinomial. ln((4 + x)(1 + x)) = 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -1x 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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