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Ln

Ln[x,α]
gives the natural logarithm, which for real evaluates on the side of the branch prescribed by .

Details and OptionsDetails and Options

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • Ln[x,α] has a branch cut discontinuity in the complex plane running from to .
  • For , the sign of determines on which side of the branch cut Ln evaluates. For all other values of x, Ln[x,α] returns Log[x].

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Compare Mathematica's built-in function Log[x] with Ln[x,α] defined by Package-X:

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Symbolically:

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Evaluate to high precision:

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Differentiate:

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