# log, xlog¶

Logarithms and natural logarithms

## log¶

Natural logarithm

Syntax: log x, log[x]

Returns the natural logarithm of x.

Null is returned if x is negative, and negative infinity where x is 0.

q)log 1
0f
q)log 0.5
-0.6931472
q)log exp 42
42f
q)log -2 0n 0 0.1 1 42
0n 0n -0w -2.302585 0 3.73767


log is an atomic function.

### Domain and range¶

domain b g x h i j e f c s p m d z n u v t
range  f . f f f f f f f . f f f z f f f f


Range: fz

## xlog¶

Logarithm

Syntax: x xlog y, xlog[x;y]

Returns the base-x logarithm of y. Where y is negative or zero, the result is null and negative infinity respectively.

q)2 xlog 8
3f
q)2 xlog 0.125
-3f
q)1.5 xlog 0 0.125 1 3 0n
-0w -5.128534 0 2.709511 0n


xlog is an atomic function.

### xlog and xexp¶

xlog is the inverse of xexp. Where both are defined, y=x xexp x xlog y.

q)2 xexp 2 xlog -1 0 0.125 1 42
0n 0 0.125 1 42


These functions return integer results from integer arguments. (Many will also accept non-integer arguments.)

### Domain and range¶

xlog | b g x h i j e f c s p m d z n u v t
---- | -----------------------------------
b    | f . f f f f f f f . f f f f f f f f
g    | . . . . . . . . . . . . . . . . . .
x    | f . f f f f f f f . f f f f f f f f
h    | f . f f f f f f f . f f f f f f f f
i    | f . f f f f f f f . f f f f f f f f
j    | f . f f f f f f f . f f f f f f f f
e    | f . f f f f f f f . f f f f f f f f
f    | f . f f f f f f f . f f f f f f f f
c    | f . f f f f f f f . f f f f f f f f
s    | . . . . . . . . . . . . . . . . . .
p    | f . f f f f f f f . f f f f f f f f
m    | f . f f f f f f f . f f f f f f f f
d    | f . f f f f f f f . f f f f f f f f
z    | f . f f f f f f f . f f f f f f f f
n    | f . f f f f f f f . f f f f f f f f
u    | f . f f f f f f f . f f f f f f f f
v    | f . f f f f f f f . f f f f f f f f
t    | f . f f f f f f f . f f f f f f f f


Range: f

Function is commutative under datatype.