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Simplifying 6ln(2x + 6) = 30 Reorder the terms: 6ln(6 + 2x) = 30 (6 * 6ln + 2x * 6ln) = 30 (36ln + 12lnx) = 30 Solving 36ln + 12lnx = 30 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -30 + 36ln + 12lnx = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 36ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + 6ln + 2lnx) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + 6ln + 2lnx)' equal to zero and attempt to solve: Simplifying -5 + 6ln + 2lnx = 0 Solving -5 + 6ln + 2lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 6ln + 5 + 2lnx = 0 + 5 Reorder the terms: -5 + 5 + 6ln + 2lnx = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6ln + 2lnx = 0 + 5 6ln + 2lnx = 0 + 5 Combine like terms: 0 + 5 = 5 6ln + 2lnx = 5 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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