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