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Simplifying 6ln(3x + 2) = 24 Reorder the terms: 6ln(2 + 3x) = 24 (2 * 6ln + 3x * 6ln) = 24 (12ln + 18lnx) = 24 Solving 12ln + 18lnx = 24 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -24 + 12ln + 18lnx = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 12ln + 18lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + 2ln + 3lnx) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + 2ln + 3lnx)' equal to zero and attempt to solve: Simplifying -4 + 2ln + 3lnx = 0 Solving -4 + 2ln + 3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 2ln + 4 + 3lnx = 0 + 4 Reorder the terms: -4 + 4 + 2ln + 3lnx = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2ln + 3lnx = 0 + 4 2ln + 3lnx = 0 + 4 Combine like terms: 0 + 4 = 4 2ln + 3lnx = 4 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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