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Simplifying 3ln(3 + -1x) + 2 = 8 (3 * 3ln + -1x * 3ln) + 2 = 8 (9ln + -3lnx) + 2 = 8 Reorder the terms: 2 + 9ln + -3lnx = 8 Solving 2 + 9ln + -3lnx = 8 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 + 9ln + -2 + -3lnx = 8 + -2 Reorder the terms: 2 + -2 + 9ln + -3lnx = 8 + -2 Combine like terms: 2 + -2 = 0 0 + 9ln + -3lnx = 8 + -2 9ln + -3lnx = 8 + -2 Combine like terms: 8 + -2 = 6 9ln + -3lnx = 6 Reorder the terms: -6 + 9ln + -3lnx = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 9ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 3ln + -1lnx) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 3ln + -1lnx)' equal to zero and attempt to solve: Simplifying -2 + 3ln + -1lnx = 0 Solving -2 + 3ln + -1lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 3ln + 2 + -1lnx = 0 + 2 Reorder the terms: -2 + 2 + 3ln + -1lnx = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3ln + -1lnx = 0 + 2 3ln + -1lnx = 0 + 2 Combine like terms: 0 + 2 = 2 3ln + -1lnx = 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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