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Simplifying 3ln(2x + 2) + 12 = 30 Reorder the terms: 3ln(2 + 2x) + 12 = 30 (2 * 3ln + 2x * 3ln) + 12 = 30 (6ln + 6lnx) + 12 = 30 Reorder the terms: 12 + 6ln + 6lnx = 30 Solving 12 + 6ln + 6lnx = 30 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 6ln + -12 + 6lnx = 30 + -12 Reorder the terms: 12 + -12 + 6ln + 6lnx = 30 + -12 Combine like terms: 12 + -12 = 0 0 + 6ln + 6lnx = 30 + -12 6ln + 6lnx = 30 + -12 Combine like terms: 30 + -12 = 18 6ln + 6lnx = 18 Reorder the terms: -18 + 6ln + 6lnx = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 6ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + ln + lnx) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + ln + lnx)' equal to zero and attempt to solve: Simplifying -3 + ln + lnx = 0 Solving -3 + ln + lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + ln + 3 + lnx = 0 + 3 Reorder the terms: -3 + 3 + ln + lnx = 0 + 3 Combine like terms: -3 + 3 = 0 0 + ln + lnx = 0 + 3 ln + lnx = 0 + 3 Combine like terms: 0 + 3 = 3 ln + lnx = 3 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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