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Simplifying ln((2x + 1)(x + 2)) = 2ln(x + 2) Reorder the terms: ln((1 + 2x)(x + 2)) = 2ln(x + 2) Reorder the terms: ln((1 + 2x)(2 + x)) = 2ln(x + 2) Multiply (1 + 2x) * (2 + x) ln((1(2 + x) + 2x * (2 + x))) = 2ln(x + 2) ln(((2 * 1 + x * 1) + 2x * (2 + x))) = 2ln(x + 2) ln(((2 + 1x) + 2x * (2 + x))) = 2ln(x + 2) ln((2 + 1x + (2 * 2x + x * 2x))) = 2ln(x + 2) ln((2 + 1x + (4x + 2x2))) = 2ln(x + 2) Combine like terms: 1x + 4x = 5x ln((2 + 5x + 2x2)) = 2ln(x + 2) (2 * ln + 5x * ln + 2x2 * ln) = 2ln(x + 2) (2ln + 5lnx + 2lnx2) = 2ln(x + 2) Reorder the terms: 2ln + 5lnx + 2lnx2 = 2ln(2 + x) 2ln + 5lnx + 2lnx2 = (2 * 2ln + x * 2ln) 2ln + 5lnx + 2lnx2 = (4ln + 2lnx) Solving 2ln + 5lnx + 2lnx2 = 4ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 2ln + 5lnx + -4ln + 2lnx2 = 4ln + -4ln + 2lnx Reorder the terms: 2ln + -4ln + 5lnx + 2lnx2 = 4ln + -4ln + 2lnx Combine like terms: 2ln + -4ln = -2ln -2ln + 5lnx + 2lnx2 = 4ln + -4ln + 2lnx Combine like terms: 4ln + -4ln = 0 -2ln + 5lnx + 2lnx2 = 0 + 2lnx -2ln + 5lnx + 2lnx2 = 2lnx Add '-2lnx' to each side of the equation. -2ln + 5lnx + -2lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: 5lnx + -2lnx = 3lnx -2ln + 3lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -2ln + 3lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + 3x + 2x2) = 0 Factor a trinomial. ln((-2 + -1x)(1 + -2x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Add 'x' to each side of the equation. -1x + x = 2 + x Combine like terms: -1x + x = 0 0 = 2 + x Simplifying 0 = 2 + 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 '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Add '2x' to each side of the equation. -2x + 2x = -1 + 2x Combine like terms: -2x + 2x = 0 0 = -1 + 2x Simplifying 0 = -1 + 2x 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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