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Simplifying (2x + -4) * ln(x + -1) = 0 Reorder the terms: (-4 + 2x) * ln(x + -1) = 0 Reorder the terms: (-4 + 2x) * ln(-1 + x) = 0 Reorder the terms for easier multiplication: ln(-4 + 2x)(-1 + x) = 0 Multiply (-4 + 2x) * (-1 + x) ln(-4(-1 + x) + 2x * (-1 + x)) = 0 ln((-1 * -4 + x * -4) + 2x * (-1 + x)) = 0 ln((4 + -4x) + 2x * (-1 + x)) = 0 ln(4 + -4x + (-1 * 2x + x * 2x)) = 0 ln(4 + -4x + (-2x + 2x2)) = 0 Combine like terms: -4x + -2x = -6x ln(4 + -6x + 2x2) = 0 (4 * ln + -6x * ln + 2x2 * ln) = 0 (4ln + -6lnx + 2lnx2) = 0 Solving 4ln + -6lnx + 2lnx2 = 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), '2ln'. 2ln(2 + -3x + x2) = 0 Factor a trinomial. 2ln((1 + -1x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 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 '(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.Subproblem 3
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. The solution to this equation could not be determined.
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