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Simplifying ln(4x + -2) + -1ln(x) + -1ln(3) = 0 Reorder the terms: ln(-2 + 4x) + -1ln(x) + -1ln(3) = 0 (-2 * ln + 4x * ln) + -1ln(x) + -1ln(3) = 0 (-2ln + 4lnx) + -1ln(x) + -1ln(3) = 0 Multiply ln * x -2ln + 4lnx + -1lnx + -1ln(3) = 0 Reorder the terms for easier multiplication: -2ln + 4lnx + -1lnx + -1 * 3ln = 0 Multiply -1 * 3 -2ln + 4lnx + -1lnx + -3ln = 0 Reorder the terms: -2ln + -3ln + 4lnx + -1lnx = 0 Combine like terms: -2ln + -3ln = -5ln -5ln + 4lnx + -1lnx = 0 Combine like terms: 4lnx + -1lnx = 3lnx -5ln + 3lnx = 0 Solving -5ln + 3lnx = 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(-5 + 3x) = 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 '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Add '-3x' to each side of the equation. 3x + -3x = 5 + -3x Combine like terms: 3x + -3x = 0 0 = 5 + -3x Simplifying 0 = 5 + -3x 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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