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Simplifying 2ln(x + 2) = 3ln(4) Reorder the terms: 2ln(2 + x) = 3ln(4) (2 * 2ln + x * 2ln) = 3ln(4) (4ln + 2lnx) = 3ln(4) Reorder the terms for easier multiplication: 4ln + 2lnx = 3 * 4ln Multiply 3 * 4 4ln + 2lnx = 12ln Solving 4ln + 2lnx = 12ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 4ln + -12ln + 2lnx = 12ln + -12ln Combine like terms: 4ln + -12ln = -8ln -8ln + 2lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -8ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-4 + 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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