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Simplifying ln(x)(x + 2) = ln(24) Reorder the terms: ln * x(2 + x) = ln(24) Multiply ln * x lnx(2 + x) = ln(24) (2 * lnx + x * lnx) = ln(24) (2lnx + lnx2) = ln(24) Reorder the terms for easier multiplication: 2lnx + lnx2 = 24ln Solving 2lnx + lnx2 = 24ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. 2lnx + -24ln + lnx2 = 24ln + -24ln Reorder the terms: -24ln + 2lnx + lnx2 = 24ln + -24ln Combine like terms: 24ln + -24ln = 0 -24ln + 2lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-24 + 2x + x2) = 0 Factor a trinomial. ln((-6 + -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 '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Add 'x' to each side of the equation. -1x + x = 6 + x Combine like terms: -1x + x = 0 0 = 6 + x Simplifying 0 = 6 + 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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