# Logarithm

(Redirected from Log)
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.[1]

## 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
```