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Simplifying ln(x2 + -8) + -1ln(8x + 1) = 0 Reorder the terms: ln(-8 + x2) + -1ln(8x + 1) = 0 (-8 * ln + x2 * ln) + -1ln(8x + 1) = 0 (-8ln + lnx2) + -1ln(8x + 1) = 0 Reorder the terms: -8ln + lnx2 + -1ln(1 + 8x) = 0 -8ln + lnx2 + (1 * -1ln + 8x * -1ln) = 0 -8ln + lnx2 + (-1ln + -8lnx) = 0 Reorder the terms: -8ln + -1ln + -8lnx + lnx2 = 0 Combine like terms: -8ln + -1ln = -9ln -9ln + -8lnx + lnx2 = 0 Solving -9ln + -8lnx + lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + -8x + x2) = 0 Factor a trinomial. ln((-1 + -1x)(9 + -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 '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + 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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