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