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Simplifying 4ln(6x + 3) + -2 = 6 Reorder the terms: 4ln(3 + 6x) + -2 = 6 (3 * 4ln + 6x * 4ln) + -2 = 6 (12ln + 24lnx) + -2 = 6 Reorder the terms: -2 + 12ln + 24lnx = 6 Solving -2 + 12ln + 24lnx = 6 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 12ln + 2 + 24lnx = 6 + 2 Reorder the terms: -2 + 2 + 12ln + 24lnx = 6 + 2 Combine like terms: -2 + 2 = 0 0 + 12ln + 24lnx = 6 + 2 12ln + 24lnx = 6 + 2 Combine like terms: 6 + 2 = 8 12ln + 24lnx = 8 Reorder the terms: -8 + 12ln + 24lnx = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 12ln + 24lnx = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 3ln + 6lnx) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + 3ln + 6lnx)' equal to zero and attempt to solve: Simplifying -2 + 3ln + 6lnx = 0 Solving -2 + 3ln + 6lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 3ln + 2 + 6lnx = 0 + 2 Reorder the terms: -2 + 2 + 3ln + 6lnx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3ln + 6lnx = 0 + 2 3ln + 6lnx = 0 + 2 Combine like terms: 0 + 2 = 2 3ln + 6lnx = 2 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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