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Simplifying 60 = 12 + 6ln(4x + 1) Reorder the terms: 60 = 12 + 6ln(1 + 4x) 60 = 12 + (1 * 6ln + 4x * 6ln) 60 = 12 + (6ln + 24lnx) Solving 60 = 12 + 6ln + 24lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 60 + -6ln = 12 + 6ln + -6ln + 24lnx Combine like terms: 6ln + -6ln = 0 60 + -6ln = 12 + 0 + 24lnx 60 + -6ln = 12 + 24lnx Add '-24lnx' to each side of the equation. 60 + -6ln + -24lnx = 12 + 24lnx + -24lnx Combine like terms: 24lnx + -24lnx = 0 60 + -6ln + -24lnx = 12 + 0 60 + -6ln + -24lnx = 12 Add '-60' to each side of the equation. 60 + -6ln + -60 + -24lnx = 12 + -60 Reorder the terms: 60 + -60 + -6ln + -24lnx = 12 + -60 Combine like terms: 60 + -60 = 0 0 + -6ln + -24lnx = 12 + -60 -6ln + -24lnx = 12 + -60 Combine like terms: 12 + -60 = -48 -6ln + -24lnx = -48 Reorder the terms: 48 + -6ln + -24lnx = -48 + 48 Combine like terms: -48 + 48 = 0 48 + -6ln + -24lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(8 + -1ln + -4lnx) = 0 Ignore the factor 6.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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