Logarithm

(Redirected from Log)
 ⍟

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.

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