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Simplifying ln((3x + 8)(x + 8)) = 2ln(x + 8) Reorder the terms: ln((8 + 3x)(x + 8)) = 2ln(x + 8) Reorder the terms: ln((8 + 3x)(8 + x)) = 2ln(x + 8) Multiply (8 + 3x) * (8 + x) ln((8(8 + x) + 3x * (8 + x))) = 2ln(x + 8) ln(((8 * 8 + x * 8) + 3x * (8 + x))) = 2ln(x + 8) ln(((64 + 8x) + 3x * (8 + x))) = 2ln(x + 8) ln((64 + 8x + (8 * 3x + x * 3x))) = 2ln(x + 8) ln((64 + 8x + (24x + 3x2))) = 2ln(x + 8) Combine like terms: 8x + 24x = 32x ln((64 + 32x + 3x2)) = 2ln(x + 8) (64 * ln + 32x * ln + 3x2 * ln) = 2ln(x + 8) (64ln + 32lnx + 3lnx2) = 2ln(x + 8) Reorder the terms: 64ln + 32lnx + 3lnx2 = 2ln(8 + x) 64ln + 32lnx + 3lnx2 = (8 * 2ln + x * 2ln) 64ln + 32lnx + 3lnx2 = (16ln + 2lnx) Solving 64ln + 32lnx + 3lnx2 = 16ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-16ln' to each side of the equation. 64ln + 32lnx + -16ln + 3lnx2 = 16ln + -16ln + 2lnx Reorder the terms: 64ln + -16ln + 32lnx + 3lnx2 = 16ln + -16ln + 2lnx Combine like terms: 64ln + -16ln = 48ln 48ln + 32lnx + 3lnx2 = 16ln + -16ln + 2lnx Combine like terms: 16ln + -16ln = 0 48ln + 32lnx + 3lnx2 = 0 + 2lnx 48ln + 32lnx + 3lnx2 = 2lnx Add '-2lnx' to each side of the equation. 48ln + 32lnx + -2lnx + 3lnx2 = 2lnx + -2lnx Combine like terms: 32lnx + -2lnx = 30lnx 48ln + 30lnx + 3lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 48ln + 30lnx + 3lnx2 = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(16 + 10x + x2) = 0 Factor a trinomial. 3ln((8 + x)(2 + x)) = 0 Ignore the factor 3.Subproblem 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 + 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.Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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