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