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Simplifying ln(4x) + -3ln(x2) = ln(2) Remove parenthesis around (4x) ln * 4x + -3ln(x2) = ln(2) Reorder the terms for easier multiplication: 4ln * x + -3ln(x2) = ln(2) Multiply ln * x 4lnx + -3ln(x2) = ln(2) Multiply ln * x2 4lnx + -3lnx2 = ln(2) Reorder the terms for easier multiplication: 4lnx + -3lnx2 = 2ln Solving 4lnx + -3lnx2 = 2ln 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. 4lnx + -2ln + -3lnx2 = 2ln + -2ln Reorder the terms: -2ln + 4lnx + -3lnx2 = 2ln + -2ln Combine like terms: 2ln + -2ln = 0 -2ln + 4lnx + -3lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + 4x + -3x2) = 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 '(-2 + 4x + -3x2)' equal to zero and attempt to solve: Simplifying -2 + 4x + -3x2 = 0 Solving -2 + 4x + -3x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 4x + 2 + -3x2 = 0 + 2 Reorder the terms: -2 + 2 + 4x + -3x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4x + -3x2 = 0 + 2 4x + -3x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4x + -3x2 = 2 Add '-4x' to each side of the equation. 4x + -4x + -3x2 = 2 + -4x Combine like terms: 4x + -4x = 0 0 + -3x2 = 2 + -4x -3x2 = 2 + -4x Add '3x2' to each side of the equation. -3x2 + 3x2 = 2 + -4x + 3x2 Combine like terms: -3x2 + 3x2 = 0 0 = 2 + -4x + 3x2 Simplifying 0 = 2 + -4x + 3x2 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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