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Simplifying ln(x) = ln(6 + -1x2) Multiply ln * x lnx = ln(6 + -1x2) lnx = (6 * ln + -1x2 * ln) lnx = (6ln + -1lnx2) Solving lnx = 6ln + -1lnx2 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 + lnx = 6ln + -6ln + -1lnx2 Combine like terms: 6ln + -6ln = 0 -6ln + lnx = 0 + -1lnx2 -6ln + lnx = -1lnx2 Add 'lnx2' to each side of the equation. -6ln + lnx + lnx2 = -1lnx2 + lnx2 Combine like terms: -1lnx2 + lnx2 = 0 -6ln + lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-6 + x + x2) = 0 Factor a trinomial. ln((-3 + -1x)(2 + -1x)) = 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 + -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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