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Simplifying 2ln(x + 3) + -1ln(x2 + 2x + -3) = 0 Reorder the terms: 2ln(3 + x) + -1ln(x2 + 2x + -3) = 0 (3 * 2ln + x * 2ln) + -1ln(x2 + 2x + -3) = 0 (6ln + 2lnx) + -1ln(x2 + 2x + -3) = 0 Reorder the terms: 6ln + 2lnx + -1ln(-3 + 2x + x2) = 0 6ln + 2lnx + (-3 * -1ln + 2x * -1ln + x2 * -1ln) = 0 6ln + 2lnx + (3ln + -2lnx + -1lnx2) = 0 Reorder the terms: 6ln + 3ln + 2lnx + -2lnx + -1lnx2 = 0 Combine like terms: 6ln + 3ln = 9ln 9ln + 2lnx + -2lnx + -1lnx2 = 0 Combine like terms: 2lnx + -2lnx = 0 9ln + 0 + -1lnx2 = 0 9ln + -1lnx2 = 0 Solving 9ln + -1lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + -1x2) = 0 Factor a difference between two squares. ln((3 + x)(3 + -1x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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