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