Log

Log[z]

gives the natural logarithm of z (logarithm to base ).

Log[b,z]

gives the logarithm to base b.

Details

  • Log is a mathematical function, suitable for both symbolic and numerical manipulation.
  • Log gives exact rational number results when possible.
  • For certain special arguments, Log automatically evaluates to exact values.
  • Log can be evaluated to arbitrary numerical precision.
  • Log automatically threads over lists.
  • Log[z] has a branch cut discontinuity in the complex z plane running from to .

Examples

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Basic Examples  (3)

Log gives the natural logarithm (to base ):

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Log[b,z] gives the logarithm to base b:

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Series expansion:

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Scope  (8)

Generalizations & Extensions  (5)

Applications  (8)

Properties & Relations  (16)

Possible Issues  (7)

Neat Examples  (6)

See Also

Log10  Log2  Exp  Power  Arg  RealExponent  MantissaExponent  ProductLog  HarmonicNumber  MultiplicativeOrder  BitLength  IntegerLength  LogPlot  PowerRange

Tutorials

Introduced in 1988
(1.0)