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Simplifying ln(x2 + -3x) = ln(18) Reorder the terms: ln(-3x + x2) = ln(18) (-3x * ln + x2 * ln) = ln(18) (-3lnx + lnx2) = ln(18) Reorder the terms for easier multiplication: -3lnx + lnx2 = 18ln Solving -3lnx + lnx2 = 18ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. -3lnx + -18ln + lnx2 = 18ln + -18ln Reorder the terms: -18ln + -3lnx + lnx2 = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 -18ln + -3lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-18 + -3x + x2) = 0 Factor a trinomial. ln((-3 + -1x)(6 + -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 '(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. The solution to this equation could not be determined.
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