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Simplifying ln(x2 + -1x) = ln(30) Reorder the terms: ln(-1x + x2) = ln(30) (-1x * ln + x2 * ln) = ln(30) (-1lnx + lnx2) = ln(30) Reorder the terms for easier multiplication: -1lnx + lnx2 = 30ln Solving -1lnx + lnx2 = 30ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-30ln' to each side of the equation. -1lnx + -30ln + lnx2 = 30ln + -30ln Reorder the terms: -30ln + -1lnx + lnx2 = 30ln + -30ln Combine like terms: 30ln + -30ln = 0 -30ln + -1lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-30 + -1x + x2) = 0 Factor a trinomial. ln((-5 + -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 '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Add 'x' to each side of the equation. -1x + x = 5 + x Combine like terms: -1x + x = 0 0 = 5 + x Simplifying 0 = 5 + 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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