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Simplifying 2ln(x + -2) + -4ln(x + 3) = 0 Reorder the terms: 2ln(-2 + x) + -4ln(x + 3) = 0 (-2 * 2ln + x * 2ln) + -4ln(x + 3) = 0 (-4ln + 2lnx) + -4ln(x + 3) = 0 Reorder the terms: -4ln + 2lnx + -4ln(3 + x) = 0 -4ln + 2lnx + (3 * -4ln + x * -4ln) = 0 -4ln + 2lnx + (-12ln + -4lnx) = 0 Reorder the terms: -4ln + -12ln + 2lnx + -4lnx = 0 Combine like terms: -4ln + -12ln = -16ln -16ln + 2lnx + -4lnx = 0 Combine like terms: 2lnx + -4lnx = -2lnx -16ln + -2lnx = 0 Solving -16ln + -2lnx = 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), '-2ln'. -2ln(8 + x) = 0 Ignore the factor -2.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. The solution to this equation could not be determined.
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