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Simplifying ln((2x + 2)(x + 8)) = 2ln(x + 8) Reorder the terms: ln((2 + 2x)(x + 8)) = 2ln(x + 8) Reorder the terms: ln((2 + 2x)(8 + x)) = 2ln(x + 8) Multiply (2 + 2x) * (8 + x) ln((2(8 + x) + 2x * (8 + x))) = 2ln(x + 8) ln(((8 * 2 + x * 2) + 2x * (8 + x))) = 2ln(x + 8) ln(((16 + 2x) + 2x * (8 + x))) = 2ln(x + 8) ln((16 + 2x + (8 * 2x + x * 2x))) = 2ln(x + 8) ln((16 + 2x + (16x + 2x2))) = 2ln(x + 8) Combine like terms: 2x + 16x = 18x ln((16 + 18x + 2x2)) = 2ln(x + 8) (16 * ln + 18x * ln + 2x2 * ln) = 2ln(x + 8) (16ln + 18lnx + 2lnx2) = 2ln(x + 8) Reorder the terms: 16ln + 18lnx + 2lnx2 = 2ln(8 + x) 16ln + 18lnx + 2lnx2 = (8 * 2ln + x * 2ln) 16ln + 18lnx + 2lnx2 = (16ln + 2lnx) Add '-16ln' to each side of the equation. 16ln + 18lnx + -16ln + 2lnx2 = 16ln + -16ln + 2lnx Reorder the terms: 16ln + -16ln + 18lnx + 2lnx2 = 16ln + -16ln + 2lnx Combine like terms: 16ln + -16ln = 0 0 + 18lnx + 2lnx2 = 16ln + -16ln + 2lnx 18lnx + 2lnx2 = 16ln + -16ln + 2lnx Combine like terms: 16ln + -16ln = 0 18lnx + 2lnx2 = 0 + 2lnx 18lnx + 2lnx2 = 2lnx Solving 18lnx + 2lnx2 = 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. 18lnx + -2lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: 18lnx + -2lnx = 16lnx 16lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 16lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2lnx'. 2lnx(8 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 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 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -1x 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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