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Simplifying 5ln(3x + 2) = 30 Reorder the terms: 5ln(2 + 3x) = 30 (2 * 5ln + 3x * 5ln) = 30 (10ln + 15lnx) = 30 Solving 10ln + 15lnx = 30 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -30 + 10ln + 15lnx = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 10ln + 15lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + 2ln + 3lnx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + 2ln + 3lnx)' equal to zero and attempt to solve: Simplifying -6 + 2ln + 3lnx = 0 Solving -6 + 2ln + 3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 2ln + 6 + 3lnx = 0 + 6 Reorder the terms: -6 + 6 + 2ln + 3lnx = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2ln + 3lnx = 0 + 6 2ln + 3lnx = 0 + 6 Combine like terms: 0 + 6 = 6 2ln + 3lnx = 6 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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