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Simplifying ln(3x + 2)(x + 2) = 2ln(x + 2) Reorder the terms: ln(2 + 3x)(x + 2) = 2ln(x + 2) Reorder the terms: ln(2 + 3x)(2 + x) = 2ln(x + 2) Multiply (2 + 3x) * (2 + x) ln(2(2 + x) + 3x * (2 + x)) = 2ln(x + 2) ln((2 * 2 + x * 2) + 3x * (2 + x)) = 2ln(x + 2) ln((4 + 2x) + 3x * (2 + x)) = 2ln(x + 2) ln(4 + 2x + (2 * 3x + x * 3x)) = 2ln(x + 2) ln(4 + 2x + (6x + 3x2)) = 2ln(x + 2) Combine like terms: 2x + 6x = 8x ln(4 + 8x + 3x2) = 2ln(x + 2) (4 * ln + 8x * ln + 3x2 * ln) = 2ln(x + 2) (4ln + 8lnx + 3lnx2) = 2ln(x + 2) Reorder the terms: 4ln + 8lnx + 3lnx2 = 2ln(2 + x) 4ln + 8lnx + 3lnx2 = (2 * 2ln + x * 2ln) 4ln + 8lnx + 3lnx2 = (4ln + 2lnx) Add '-4ln' to each side of the equation. 4ln + 8lnx + -4ln + 3lnx2 = 4ln + -4ln + 2lnx Reorder the terms: 4ln + -4ln + 8lnx + 3lnx2 = 4ln + -4ln + 2lnx Combine like terms: 4ln + -4ln = 0 0 + 8lnx + 3lnx2 = 4ln + -4ln + 2lnx 8lnx + 3lnx2 = 4ln + -4ln + 2lnx Combine like terms: 4ln + -4ln = 0 8lnx + 3lnx2 = 0 + 2lnx 8lnx + 3lnx2 = 2lnx Solving 8lnx + 3lnx2 = 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. 8lnx + -2lnx + 3lnx2 = 2lnx + -2lnx Combine like terms: 8lnx + -2lnx = 6lnx 6lnx + 3lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 6lnx + 3lnx2 = 0 Factor out the Greatest Common Factor (GCF), '3lnx'. 3lnx(2 + x) = 0 Ignore the factor 3.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 '(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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