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Simplifying ln(3x2 + -10x + 8) + -1ln(x2 + -5x + 6) = ln * 2x Reorder the terms: ln(8 + -10x + 3x2) + -1ln(x2 + -5x + 6) = ln * 2x (8 * ln + -10x * ln + 3x2 * ln) + -1ln(x2 + -5x + 6) = ln * 2x (8ln + -10lnx + 3lnx2) + -1ln(x2 + -5x + 6) = ln * 2x Reorder the terms: 8ln + -10lnx + 3lnx2 + -1ln(6 + -5x + x2) = ln * 2x 8ln + -10lnx + 3lnx2 + (6 * -1ln + -5x * -1ln + x2 * -1ln) = ln * 2x 8ln + -10lnx + 3lnx2 + (-6ln + 5lnx + -1lnx2) = ln * 2x Reorder the terms: 8ln + -6ln + -10lnx + 5lnx + 3lnx2 + -1lnx2 = ln * 2x Combine like terms: 8ln + -6ln = 2ln 2ln + -10lnx + 5lnx + 3lnx2 + -1lnx2 = ln * 2x Combine like terms: -10lnx + 5lnx = -5lnx 2ln + -5lnx + 3lnx2 + -1lnx2 = ln * 2x Combine like terms: 3lnx2 + -1lnx2 = 2lnx2 2ln + -5lnx + 2lnx2 = ln * 2x Reorder the terms for easier multiplication: 2ln + -5lnx + 2lnx2 = 2ln * x Multiply ln * x 2ln + -5lnx + 2lnx2 = 2lnx Solving 2ln + -5lnx + 2lnx2 = 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnx' to each side of the equation. 2ln + -5lnx + -2lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: -5lnx + -2lnx = -7lnx 2ln + -7lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 2ln + -7lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2 + -7x + 2x2) = 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 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying 2 + -7x + 2x2 = 0 Solving 2 + -7x + 2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -7x + -2 + 2x2 = 0 + -2 Reorder the terms: 2 + -2 + -7x + 2x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x + 2x2 = 0 + -2 -7x + 2x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7x + 2x2 = -2 Add '7x' to each side of the equation. -7x + 7x + 2x2 = -2 + 7x Combine like terms: -7x + 7x = 0 0 + 2x2 = -2 + 7x 2x2 = -2 + 7x Add '-2x2' to each side of the equation. 2x2 + -2x2 = -2 + 7x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = -2 + 7x + -2x2 Simplifying 0 = -2 + 7x + -2x2 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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