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Simplifying 5ln(2x + 3) + -2 = 8 Reorder the terms: 5ln(3 + 2x) + -2 = 8 (3 * 5ln + 2x * 5ln) + -2 = 8 (15ln + 10lnx) + -2 = 8 Reorder the terms: -2 + 15ln + 10lnx = 8 Solving -2 + 15ln + 10lnx = 8 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 15ln + 2 + 10lnx = 8 + 2 Reorder the terms: -2 + 2 + 15ln + 10lnx = 8 + 2 Combine like terms: -2 + 2 = 0 0 + 15ln + 10lnx = 8 + 2 15ln + 10lnx = 8 + 2 Combine like terms: 8 + 2 = 10 15ln + 10lnx = 10 Reorder the terms: -10 + 15ln + 10lnx = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 15ln + 10lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 3ln + 2lnx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + 3ln + 2lnx)' equal to zero and attempt to solve: Simplifying -2 + 3ln + 2lnx = 0 Solving -2 + 3ln + 2lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 3ln + 2 + 2lnx = 0 + 2 Reorder the terms: -2 + 2 + 3ln + 2lnx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3ln + 2lnx = 0 + 2 3ln + 2lnx = 0 + 2 Combine like terms: 0 + 2 = 2 3ln + 2lnx = 2 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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