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Simplifying 2lnx + -2lnx + 3ln = 5lnx + -1lnx + 2ln Reorder the terms: 3ln + 2lnx + -2lnx = 5lnx + -1lnx + 2ln Combine like terms: 2lnx + -2lnx = 0 3ln + 0 = 5lnx + -1lnx + 2ln 3ln = 5lnx + -1lnx + 2ln Reorder the terms: 3ln = 2ln + 5lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx 3ln = 2ln + 4lnx Solving 3ln = 2ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. 3ln + -2ln = 2ln + -2ln + 4lnx Combine like terms: 3ln + -2ln = 1ln 1ln = 2ln + -2ln + 4lnx Combine like terms: 2ln + -2ln = 0 1ln = 0 + 4lnx 1ln = 4lnx Add '-4lnx' to each side of the equation. 1ln + -4lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 1ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -4x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Add '4x' to each side of the equation. -4x + 4x = -1 + 4x Combine like terms: -4x + 4x = 0 0 = -1 + 4x Simplifying 0 = -1 + 4x 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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