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Simplifying ln(-4x) = ln(x2 + -32) Remove parenthesis around (-4x) ln * -4x = ln(x2 + -32) Reorder the terms for easier multiplication: -4ln * x = ln(x2 + -32) Multiply ln * x -4lnx = ln(x2 + -32) Reorder the terms: -4lnx = ln(-32 + x2) -4lnx = (-32 * ln + x2 * ln) -4lnx = (-32ln + lnx2) Solving -4lnx = -32ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '32ln' to each side of the equation. 32ln + -4lnx = -32ln + 32ln + lnx2 Combine like terms: -32ln + 32ln = 0 32ln + -4lnx = 0 + lnx2 32ln + -4lnx = lnx2 Add '-1lnx2' to each side of the equation. 32ln + -4lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 32ln + -4lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(32 + -4x + -1x2) = 0 Factor a trinomial. ln((4 + -1x)(8 + 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 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -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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