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Simplifying 4ln(6x + 3) + 8 = 20 Reorder the terms: 4ln(3 + 6x) + 8 = 20 (3 * 4ln + 6x * 4ln) + 8 = 20 (12ln + 24lnx) + 8 = 20 Reorder the terms: 8 + 12ln + 24lnx = 20 Solving 8 + 12ln + 24lnx = 20 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + 12ln + -8 + 24lnx = 20 + -8 Reorder the terms: 8 + -8 + 12ln + 24lnx = 20 + -8 Combine like terms: 8 + -8 = 0 0 + 12ln + 24lnx = 20 + -8 12ln + 24lnx = 20 + -8 Combine like terms: 20 + -8 = 12 12ln + 24lnx = 12 Reorder the terms: -12 + 12ln + 24lnx = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 12ln + 24lnx = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-1 + ln + 2lnx) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-1 + ln + 2lnx)' equal to zero and attempt to solve: Simplifying -1 + ln + 2lnx = 0 Solving -1 + ln + 2lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + ln + 1 + 2lnx = 0 + 1 Reorder the terms: -1 + 1 + ln + 2lnx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + ln + 2lnx = 0 + 1 ln + 2lnx = 0 + 1 Combine like terms: 0 + 1 = 1 ln + 2lnx = 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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