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Simplifying ln(2x + -1) + 2ln(x) = 0 Reorder the terms: ln(-1 + 2x) + 2ln(x) = 0 (-1 * ln + 2x * ln) + 2ln(x) = 0 (-1ln + 2lnx) + 2ln(x) = 0 Multiply ln * x -1ln + 2lnx + 2lnx = 0 Combine like terms: 2lnx + 2lnx = 4lnx -1ln + 4lnx = 0 Solving -1ln + 4lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. 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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