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