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Simplifying 2lnx + 3ln(x + 4) = 0 Reorder the terms: 2lnx + 3ln(4 + x) = 0 2lnx + (4 * 3ln + x * 3ln) = 0 2lnx + (12ln + 3lnx) = 0 Reorder the terms: 12ln + 2lnx + 3lnx = 0 Combine like terms: 2lnx + 3lnx = 5lnx 12ln + 5lnx = 0 Solving 12ln + 5lnx = 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(12 + 5x) = 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 '(12 + 5x)' equal to zero and attempt to solve: Simplifying 12 + 5x = 0 Solving 12 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 5x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 5x = 0 + -12 5x = 0 + -12 Combine like terms: 0 + -12 = -12 5x = -12 Add '-5x' to each side of the equation. 5x + -5x = -12 + -5x Combine like terms: 5x + -5x = 0 0 = -12 + -5x Simplifying 0 = -12 + -5x 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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