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# log1p

Logarithm functions
View other versions (5)

## Interface

`#include <math.h>double log (double x)long logl (long double x)float logf (float x)double log2 (double x)long log2l (long double x)float log2f (float x)double log10 (double x)long log10l (long double x)float log10f (float x)double log1p (double x)long log1pl (long double x)float log1pf (float x)`

## Description

The log function computes the value of the natural logarithm of argument x.

The log2 function computes the value of the logarithm of argument x to base 2.

The log10 function computes the value of the logarithm of argument x to base 10.

The log1p function computes the value of accurately even for very small values of x.

Example:
##### Example - Logarithm functions
Workings
```#include <math.h>
#include <stdio.h>
int main()
{
printf("\n   x    \t   log   \t   log2   \t   log10   \t   log1p");
for(double x=0; x<=10; x+=0.5)
printf("\n%lf\t%lf\t%lf\t%lf\t%lf", x, log(x), log2(x), log10(x), log1p(x));
return 0;
}```
Solution
Output
```x    	   log   	   log2   	   log10   	   log1p
0.000000	-inf	        -inf	        -inf	        0.000000
0.500000	-0.693147	-1.000000	-0.301030	0.405465
1.000000	0.000000	0.000000	0.000000	0.693147
1.500000	0.405465	0.584963	0.176091	0.916291
2.000000	0.693147	1.000000	0.301030	1.098612
2.500000	0.916291	1.321928	0.397940	1.252763
3.000000	1.098612	1.584963	0.477121	1.386294
3.500000	1.252763	1.807355	0.544068	1.504077
4.000000	1.386294	2.000000	0.602060	1.609438
4.500000	1.504077	2.169925	0.653213	1.704748
5.000000	1.609438	2.321928	0.698970	1.791759
5.500000	1.704748	2.459432	0.740363	1.871802
6.000000	1.791759	2.584963	0.778151	1.945910
6.500000	1.871802	2.700440	0.812913	2.014903
7.000000	1.945910	2.807355	0.845098	2.079442
7.500000	2.014903	2.906891	0.875061	2.140066
8.000000	2.079442	3.000000	0.903090	2.197225
8.500000	2.140066	3.087463	0.929419	2.251292
9.000000	2.197225	3.169925	0.954243	2.302585
9.500000	2.251292	3.247928	0.977724	2.351375
10.000000	2.302585	3.321928	1.000000	2.397895```

## Special Values

log ( ±0 ), log2 ( ±0 ), and log10( ±0 ) return -∞ and raise the divide-by-zero floating-point exception.

log ( 1 ), log2 ( 1 ), and log10 ( 1 ) return +0.

log ( x ), log2 ( x ), and log10 ( x ) return a NaN and raise the invalid floating-point exception for x < 0.

log ( +∞ ), log2 ( +∞ ), and log10 ( +∞ ) return +∞.

log1p ( ±0 ) returns ±0.

log1p ( -1 ) returns -∞ and raises the divide-by-zero floating-point exception.

log1p ( x ) returns a NaN and raises the invalid floating-point exception for x < -1.

log1p ( +∞ ) returns +∞.