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Simplifying 54 = 14 + 5ln(4x + 1) Reorder the terms: 54 = 14 + 5ln(1 + 4x) 54 = 14 + (1 * 5ln + 4x * 5ln) 54 = 14 + (5ln + 20lnx) Solving 54 = 14 + 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. 54 + -5ln = 14 + 5ln + -5ln + 20lnx Combine like terms: 5ln + -5ln = 0 54 + -5ln = 14 + 0 + 20lnx 54 + -5ln = 14 + 20lnx Add '-20lnx' to each side of the equation. 54 + -5ln + -20lnx = 14 + 20lnx + -20lnx Combine like terms: 20lnx + -20lnx = 0 54 + -5ln + -20lnx = 14 + 0 54 + -5ln + -20lnx = 14 Add '-54' to each side of the equation. 54 + -5ln + -54 + -20lnx = 14 + -54 Reorder the terms: 54 + -54 + -5ln + -20lnx = 14 + -54 Combine like terms: 54 + -54 = 0 0 + -5ln + -20lnx = 14 + -54 -5ln + -20lnx = 14 + -54 Combine like terms: 14 + -54 = -40 -5ln + -20lnx = -40 Reorder the terms: 40 + -5ln + -20lnx = -40 + 40 Combine like terms: -40 + 40 = 0 40 + -5ln + -20lnx = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(8 + -1ln + -4lnx) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8 + -1ln + -4lnx)' equal to zero and attempt to solve: Simplifying 8 + -1ln + -4lnx = 0 Solving 8 + -1ln + -4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -1ln + -8 + -4lnx = 0 + -8 Reorder the terms: 8 + -8 + -1ln + -4lnx = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1ln + -4lnx = 0 + -8 -1ln + -4lnx = 0 + -8 Combine like terms: 0 + -8 = -8 -1ln + -4lnx = -8 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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