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Simplifying 2ln(4x + -1) + 4 = 6 Reorder the terms: 2ln(-1 + 4x) + 4 = 6 (-1 * 2ln + 4x * 2ln) + 4 = 6 (-2ln + 8lnx) + 4 = 6 Reorder the terms: 4 + -2ln + 8lnx = 6 Solving 4 + -2ln + 8lnx = 6 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -2ln + -4 + 8lnx = 6 + -4 Reorder the terms: 4 + -4 + -2ln + 8lnx = 6 + -4 Combine like terms: 4 + -4 = 0 0 + -2ln + 8lnx = 6 + -4 -2ln + 8lnx = 6 + -4 Combine like terms: 6 + -4 = 2 -2ln + 8lnx = 2 Reorder the terms: -2 + -2ln + 8lnx = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -2ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -1ln + 4lnx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1ln + 4lnx)' equal to zero and attempt to solve: Simplifying -1 + -1ln + 4lnx = 0 Solving -1 + -1ln + 4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1ln + 1 + 4lnx = 0 + 1 Reorder the terms: -1 + 1 + -1ln + 4lnx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1ln + 4lnx = 0 + 1 -1ln + 4lnx = 0 + 1 Combine like terms: 0 + 1 = 1 -1ln + 4lnx = 1 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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