# log, xlog¶

Logarithms and natural logarithms

## log¶

Natural logarithm

log x    log[x]

Where x is numeric and

• null, returns null
• 0, returns -0w
• a datetime, returns x
• otherwise, the natural logarithm of x
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

### Implicit iteration¶

log is an atomic function. It applies to dictionaries and tables

q)log(2;3 4)
0.6931472
1.098612 1.386294

q)k:k xkey update k:abcdefghi from t:flip d:ab!(10 -21 3;4 5 -6)

q)log d
a| 2.302585          1.098612
b| 1.386294 1.609438

q)log t
a        b
-----------------
2.302585 1.386294
1.609438
1.098612

q)log k
k  | a        b
---| -----------------
abc| 2.302585 1.386294
def|          1.609438
ghi| 1.098612

### 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

x xlog y    xlog[x;y]

Returns the base-xf logarithm of yf, where xf and yf are x and y cast to floats, i.e. "f"$(x;y). Where yf is negative or zero, the result is null and negative infinity respectively. q)2 xlog 8 3f q)2 xlog 0.125 -3f q)1.5 xlog 0 0.125 1 3 0n -0w -5.128534 0 2.709511 0n q)float$"AC"
65 67f
q)65 xlog 67
1.00726
q)"A"xlog"C"
1.00726

### Implicit iteration¶

xlog is an atomic function. It applies to dictionaries and tables

q)(2;3 4)xlog(4;5 6)
2f
1.464974 1.292481

q)10 xlog d
a| 1               0.4771213
b| 0.60206 0.69897

q)10 xlog t
a         b
-----------------
1         0.60206
0.69897
0.4771213

q)10 xlog k
k  | a         b
---| -----------------
abc| 1         0.60206
def|           0.69897
ghi| 0.4771213

### xlog and xexp¶

xlog is the inverse of xexp, i.e. y~x xexp x xlog y.

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

### 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
g    | . . . . . . . . . . . . . . . . . .
x    | 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
i    | 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
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
c    | 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
m    | 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
z    | . . . . . . . . . . . . . . . . . .
n    | 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
v    | 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

Range: f`