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Simplifying ln(x + 8)(x + -1) = 2lnx Reorder the terms: ln(8 + x)(x + -1) = 2lnx Reorder the terms: ln(8 + x)(-1 + x) = 2lnx Multiply (8 + x) * (-1 + x) ln(8(-1 + x) + x(-1 + x)) = 2lnx ln((-1 * 8 + x * 8) + x(-1 + x)) = 2lnx ln((-8 + 8x) + x(-1 + x)) = 2lnx ln(-8 + 8x + (-1 * x + x * x)) = 2lnx ln(-8 + 8x + (-1x + x2)) = 2lnx Combine like terms: 8x + -1x = 7x ln(-8 + 7x + x2) = 2lnx (-8 * ln + 7x * ln + x2 * ln) = 2lnx (-8ln + 7lnx + lnx2) = 2lnx Solving -8ln + 7lnx + lnx2 = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. -8ln + 7lnx + -2lnx + lnx2 = 2lnx + -2lnx Combine like terms: 7lnx + -2lnx = 5lnx -8ln + 5lnx + lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -8ln + 5lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 5x + x2) = 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 '(-8 + 5x + x2)' equal to zero and attempt to solve: Simplifying -8 + 5x + x2 = 0 Solving -8 + 5x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5x + x2 = 0 + 8 5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 5x + x2 = 8 Add '-5x' to each side of the equation. 5x + -5x + x2 = 8 + -5x Combine like terms: 5x + -5x = 0 0 + x2 = 8 + -5x x2 = 8 + -5x Add '-1x2' to each side of the equation. x2 + -1x2 = 8 + -5x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 8 + -5x + -1x2 Simplifying 0 = 8 + -5x + -1x2 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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