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Simplifying 3ln(2) = ln(x + -3)(x + -1) Reorder the terms for easier multiplication: 3 * 2ln = ln(x + -3)(x + -1) Multiply 3 * 2 6ln = ln(x + -3)(x + -1) Reorder the terms: 6ln = ln(-3 + x)(x + -1) Reorder the terms: 6ln = ln(-3 + x)(-1 + x) Multiply (-3 + x) * (-1 + x) 6ln = ln(-3(-1 + x) + x(-1 + x)) 6ln = ln((-1 * -3 + x * -3) + x(-1 + x)) 6ln = ln((3 + -3x) + x(-1 + x)) 6ln = ln(3 + -3x + (-1 * x + x * x)) 6ln = ln(3 + -3x + (-1x + x2)) Combine like terms: -3x + -1x = -4x 6ln = ln(3 + -4x + x2) 6ln = (3 * ln + -4x * ln + x2 * ln) 6ln = (3ln + -4lnx + lnx2) Solving 6ln = 3ln + -4lnx + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 6ln + -3ln = 3ln + -4lnx + -3ln + lnx2 Combine like terms: 6ln + -3ln = 3ln 3ln = 3ln + -4lnx + -3ln + lnx2 Reorder the terms: 3ln = 3ln + -3ln + -4lnx + lnx2 Combine like terms: 3ln + -3ln = 0 3ln = 0 + -4lnx + lnx2 3ln = -4lnx + lnx2 Add '4lnx' to each side of the equation. 3ln + 4lnx = -4lnx + 4lnx + lnx2 Combine like terms: -4lnx + 4lnx = 0 3ln + 4lnx = 0 + lnx2 3ln + 4lnx = lnx2 Add '-1lnx2' to each side of the equation. 3ln + 4lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 3ln + 4lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + 4x + -1x2) = 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 '(3 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + -1x2 = 0 Solving 3 + 4x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 4x + -3 + -1x2 = 0 + -3 Reorder the terms: 3 + -3 + 4x + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x + -1x2 = 0 + -3 4x + -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 4x + -1x2 = -3 Add '-4x' to each side of the equation. 4x + -4x + -1x2 = -3 + -4x Combine like terms: 4x + -4x = 0 0 + -1x2 = -3 + -4x -1x2 = -3 + -4x Add 'x2' to each side of the equation. -1x2 + x2 = -3 + -4x + x2 Combine like terms: -1x2 + x2 = 0 0 = -3 + -4x + x2 Simplifying 0 = -3 + -4x + x2 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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