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Simplifying x2 * ln(2) + -1x * ln(3) = ln(2) Reorder the terms for easier multiplication: 2x2 * ln + -1x * ln(3) = ln(2) Multiply x2 * ln 2lnx2 + -1x * ln(3) = ln(2) Reorder the terms for easier multiplication: 2lnx2 + -1 * 3x * ln = ln(2) Multiply -1 * 3 2lnx2 + -3x * ln = ln(2) Multiply x * ln 2lnx2 + -3lnx = ln(2) Reorder the terms: -3lnx + 2lnx2 = ln(2) Reorder the terms for easier multiplication: -3lnx + 2lnx2 = 2ln Solving -3lnx + 2lnx2 = 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. -3lnx + -2ln + 2lnx2 = 2ln + -2ln Reorder the terms: -2ln + -3lnx + 2lnx2 = 2ln + -2ln Combine like terms: 2ln + -2ln = 0 -2ln + -3lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + -3x + 2x2) = 0 Factor a trinomial. ln((-1 + -2x)(2 + -1x)) = 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 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Add '2x' to each side of the equation. -2x + 2x = 1 + 2x Combine like terms: -2x + 2x = 0 0 = 1 + 2x Simplifying 0 = 1 + 2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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