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Simplifying 39 = 9 + 5ln(4x + 1) Reorder the terms: 39 = 9 + 5ln(1 + 4x) 39 = 9 + (1 * 5ln + 4x * 5ln) 39 = 9 + (5ln + 20lnx) Solving 39 = 9 + 5ln + 20lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 39 + -5ln = 9 + 5ln + -5ln + 20lnx Combine like terms: 5ln + -5ln = 0 39 + -5ln = 9 + 0 + 20lnx 39 + -5ln = 9 + 20lnx Add '-20lnx' to each side of the equation. 39 + -5ln + -20lnx = 9 + 20lnx + -20lnx Combine like terms: 20lnx + -20lnx = 0 39 + -5ln + -20lnx = 9 + 0 39 + -5ln + -20lnx = 9 Add '-39' to each side of the equation. 39 + -5ln + -39 + -20lnx = 9 + -39 Reorder the terms: 39 + -39 + -5ln + -20lnx = 9 + -39 Combine like terms: 39 + -39 = 0 0 + -5ln + -20lnx = 9 + -39 -5ln + -20lnx = 9 + -39 Combine like terms: 9 + -39 = -30 -5ln + -20lnx = -30 Reorder the terms: 30 + -5ln + -20lnx = -30 + 30 Combine like terms: -30 + 30 = 0 30 + -5ln + -20lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(6 + -1ln + -4lnx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + -1ln + -4lnx)' equal to zero and attempt to solve: Simplifying 6 + -1ln + -4lnx = 0 Solving 6 + -1ln + -4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -1ln + -6 + -4lnx = 0 + -6 Reorder the terms: 6 + -6 + -1ln + -4lnx = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1ln + -4lnx = 0 + -6 -1ln + -4lnx = 0 + -6 Combine like terms: 0 + -6 = -6 -1ln + -4lnx = -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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