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Simplifying lnx2 = ln(6x + -8) Reorder the terms: lnx2 = ln(-8 + 6x) lnx2 = (-8 * ln + 6x * ln) lnx2 = (-8ln + 6lnx) Solving lnx2 = -8ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8ln' to each side of the equation. 8ln + lnx2 = -8ln + 8ln + 6lnx Combine like terms: -8ln + 8ln = 0 8ln + lnx2 = 0 + 6lnx 8ln + lnx2 = 6lnx Add '-6lnx' to each side of the equation. 8ln + -6lnx + lnx2 = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 8ln + -6lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(8 + -6x + x2) = 0 Factor a trinomial. ln((2 + -1x)(4 + -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 '(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 '(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. The solution to this equation could not be determined.
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