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, X⍟Y
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.
Examples
2⍟0.5 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)
┌─┬─────────────┐
│7│1 1 0 0 1 0 0│
└─┴─────────────┘
(10 Digits 100) (10 ToBase 100)
┌─┬─────┐
│3│1 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
2⍟2 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