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Simplifying 2ln(3x + 4) + 5 = 17 Reorder the terms: 2ln(4 + 3x) + 5 = 17 (4 * 2ln + 3x * 2ln) + 5 = 17 (8ln + 6lnx) + 5 = 17 Reorder the terms: 5 + 8ln + 6lnx = 17 Solving 5 + 8ln + 6lnx = 17 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 8ln + -5 + 6lnx = 17 + -5 Reorder the terms: 5 + -5 + 8ln + 6lnx = 17 + -5 Combine like terms: 5 + -5 = 0 0 + 8ln + 6lnx = 17 + -5 8ln + 6lnx = 17 + -5 Combine like terms: 17 + -5 = 12 8ln + 6lnx = 12 Reorder the terms: -12 + 8ln + 6lnx = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 8ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 4ln + 3lnx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 4ln + 3lnx)' equal to zero and attempt to solve: Simplifying -6 + 4ln + 3lnx = 0 Solving -6 + 4ln + 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 + 4ln + 6 + 3lnx = 0 + 6 Reorder the terms: -6 + 6 + 4ln + 3lnx = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4ln + 3lnx = 0 + 6 4ln + 3lnx = 0 + 6 Combine like terms: 0 + 6 = 6 4ln + 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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