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Simplifying 4ln(x2 + -3) + -1ln(x4 + -9) = 0 Reorder the terms: 4ln(-3 + x2) + -1ln(x4 + -9) = 0 (-3 * 4ln + x2 * 4ln) + -1ln(x4 + -9) = 0 (-12ln + 4lnx2) + -1ln(x4 + -9) = 0 Reorder the terms: -12ln + 4lnx2 + -1ln(-9 + x4) = 0 -12ln + 4lnx2 + (-9 * -1ln + x4 * -1ln) = 0 -12ln + 4lnx2 + (9ln + -1lnx4) = 0 Reorder the terms: -12ln + 9ln + 4lnx2 + -1lnx4 = 0 Combine like terms: -12ln + 9ln = -3ln -3ln + 4lnx2 + -1lnx4 = 0 Solving -3ln + 4lnx2 + -1lnx4 = 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(-3 + 4x2 + -1x4) = 0 Factor a trinomial. ln((-3 + x2)(1 + -1x2)) = 0 Factor a difference between two squares. ln((-3 + x2)((1 + x)(1 + -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 + x2)' equal to zero and attempt to solve: Simplifying -3 + x2 = 0 Solving -3 + x2 = 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 + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 0 + 3 x2 = 0 + 3 Combine like terms: 0 + 3 = 3 x2 = 3 Add '-1x2' to each side of the equation. x2 + -1x2 = 3 + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 3 + -1x2 Simplifying 0 = 3 + -1x2 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.Subproblem 4
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + 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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