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Simplifying ln(x + -4)(x + 1) = ln(x + 8) Reorder the terms: ln(-4 + x)(x + 1) = ln(x + 8) Reorder the terms: ln(-4 + x)(1 + x) = ln(x + 8) Multiply (-4 + x) * (1 + x) ln(-4(1 + x) + x(1 + x)) = ln(x + 8) ln((1 * -4 + x * -4) + x(1 + x)) = ln(x + 8) ln((-4 + -4x) + x(1 + x)) = ln(x + 8) ln(-4 + -4x + (1 * x + x * x)) = ln(x + 8) ln(-4 + -4x + (1x + x2)) = ln(x + 8) Combine like terms: -4x + 1x = -3x ln(-4 + -3x + x2) = ln(x + 8) (-4 * ln + -3x * ln + x2 * ln) = ln(x + 8) (-4ln + -3lnx + lnx2) = ln(x + 8) Reorder the terms: -4ln + -3lnx + lnx2 = ln(8 + x) -4ln + -3lnx + lnx2 = (8 * ln + x * ln) -4ln + -3lnx + lnx2 = (8ln + lnx) Solving -4ln + -3lnx + lnx2 = 8ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. -4ln + -3lnx + -8ln + lnx2 = 8ln + -8ln + lnx Reorder the terms: -4ln + -8ln + -3lnx + lnx2 = 8ln + -8ln + lnx Combine like terms: -4ln + -8ln = -12ln -12ln + -3lnx + lnx2 = 8ln + -8ln + lnx Combine like terms: 8ln + -8ln = 0 -12ln + -3lnx + lnx2 = 0 + lnx -12ln + -3lnx + lnx2 = lnx Add '-1lnx' to each side of the equation. -12ln + -3lnx + -1lnx + lnx2 = lnx + -1lnx Combine like terms: -3lnx + -1lnx = -4lnx -12ln + -4lnx + lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -12ln + -4lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-12 + -4x + x2) = 0 Factor a trinomial. ln((-2 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + 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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