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Simplifying 6ln(4x + 2) + 6 = 18 Reorder the terms: 6ln(2 + 4x) + 6 = 18 (2 * 6ln + 4x * 6ln) + 6 = 18 (12ln + 24lnx) + 6 = 18 Reorder the terms: 6 + 12ln + 24lnx = 18 Solving 6 + 12ln + 24lnx = 18 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 12ln + -6 + 24lnx = 18 + -6 Reorder the terms: 6 + -6 + 12ln + 24lnx = 18 + -6 Combine like terms: 6 + -6 = 0 0 + 12ln + 24lnx = 18 + -6 12ln + 24lnx = 18 + -6 Combine like terms: 18 + -6 = 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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