Logarithm

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This page describes the dyadic arithmetic function. For the monadic natural logarithm function, see Natural Logarithm.

Logarithm (), or Log, is a dyadic scalar function which computes the logarithm of the two arguments. More precisely, XY computes how much power of X equals Y, i.e. the value of R that satisfies Y=X*R. Logarithm shares the glyph with the monadic arithmetic function Natural Logarithm. The glyph, a composition of the glyphs for Circular () and Power (*) to indicate its close mathematical ties with these two functions, is a stylised tree log.[1]

Examples

      20.5 1 2 32 1024
¯1 0 1 5 10

Logarithm can be used to determine how many digits are needed to write a positive integer Y in base X:

      Digits{1+⌊}
      ToBase¯1
      (2 Digits 100) (2 ToBase 100)
┌─┬─────────────┐
71 1 0 0 1 0 0
└─┴─────────────┘
      (10 Digits 100) (10 ToBase 100)
┌─┬─────┐
31 0 0
└─┴─────┘
Works in: Dyalog APL

Properties

By definition, logarithm is the inverse of the power with the same base (left argument).

      2*1 2 3 4 5
2 4 8 16 32
      22 4 8 16 32
1 2 3 4 5
      2 (*¯1  ) 10
1
Works in: Dyalog APL

Reciprocal on the left or right argument gives the negated result.

      2⍟÷2 4 8 16 32
¯1 ¯2 ¯3 ¯4 ¯5
      (÷2)2 4 8 16 32
¯1 ¯2 ¯3 ¯4 ¯5

See also

External links

Documentation

References

APL built-ins [edit]
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
Operators SearchReplace