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