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