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Simplifying ln(x2 + -1) = ln(x + 1) + ln(x) Reorder the terms: ln(-1 + x2) = ln(x + 1) + ln(x) (-1 * ln + x2 * ln) = ln(x + 1) + ln(x) (-1ln + lnx2) = ln(x + 1) + ln(x) Reorder the terms: -1ln + lnx2 = ln(1 + x) + ln(x) -1ln + lnx2 = (1 * ln + x * ln) + ln(x) -1ln + lnx2 = (1ln + lnx) + ln(x) Multiply ln * x -1ln + lnx2 = 1ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx -1ln + lnx2 = 1ln + 2lnx Solving -1ln + lnx2 = 1ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. -1ln + -1ln + lnx2 = 1ln + -1ln + 2lnx Combine like terms: -1ln + -1ln = -2ln -2ln + lnx2 = 1ln + -1ln + 2lnx Combine like terms: 1ln + -1ln = 0 -2ln + lnx2 = 0 + 2lnx -2ln + lnx2 = 2lnx Add '-2lnx' to each side of the equation. -2ln + -2lnx + lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 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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