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