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Simplifying 4ln(3x + 8) = 10 Reorder the terms: 4ln(8 + 3x) = 10 (8 * 4ln + 3x * 4ln) = 10 (32ln + 12lnx) = 10 Solving 32ln + 12lnx = 10 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -10 + 32ln + 12lnx = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 32ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 16ln + 6lnx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 16ln + 6lnx)' equal to zero and attempt to solve: Simplifying -5 + 16ln + 6lnx = 0 Solving -5 + 16ln + 6lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 16ln + 5 + 6lnx = 0 + 5 Reorder the terms: -5 + 5 + 16ln + 6lnx = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 16ln + 6lnx = 0 + 5 16ln + 6lnx = 0 + 5 Combine like terms: 0 + 5 = 5 16ln + 6lnx = 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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