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