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Simplifying 6ln(3x + 1) = 12 Reorder the terms: 6ln(1 + 3x) = 12 (1 * 6ln + 3x * 6ln) = 12 (6ln + 18lnx) = 12 Solving 6ln + 18lnx = 12 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Reorder the terms: -12 + 6ln + 18lnx = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 6ln + 18lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + ln + 3lnx) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + ln + 3lnx)' equal to zero and attempt to solve: Simplifying -2 + ln + 3lnx = 0 Solving -2 + ln + 3lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + ln + 2 + 3lnx = 0 + 2 Reorder the terms: -2 + 2 + ln + 3lnx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + ln + 3lnx = 0 + 2 ln + 3lnx = 0 + 2 Combine like terms: 0 + 2 = 2 ln + 3lnx = 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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