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Simplifying 6ln(4x + 1) = 14 Reorder the terms: 6ln(1 + 4x) = 14 (1 * 6ln + 4x * 6ln) = 14 (6ln + 24lnx) = 14 Solving 6ln + 24lnx = 14 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -14 + 6ln + 24lnx = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 6ln + 24lnx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 3ln + 12lnx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 3ln + 12lnx)' equal to zero and attempt to solve: Simplifying -7 + 3ln + 12lnx = 0 Solving -7 + 3ln + 12lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 3ln + 7 + 12lnx = 0 + 7 Reorder the terms: -7 + 7 + 3ln + 12lnx = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3ln + 12lnx = 0 + 7 3ln + 12lnx = 0 + 7 Combine like terms: 0 + 7 = 7 3ln + 12lnx = 7 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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