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log, logf, logl, log10, log10f, log10l

Calculates logarithms.


double log(double x);
float logf(float x);
long double logl(double x);
double log10(double x);
float log10f (float x);
long double log10l(double x);
#define log(X) // Requires C11 or higher
#define log10(X) // Requires C11 or higher

float log(float x);  // C++ only
long double log(long double x);  // C++ only
float log10(float x);  // C++ only
long double log10(long double x);  // C++ only


Value whose logarithm is to be found.

Return value

The log functions return the natural logarithm (base e) of x if successful. The log10 functions return the base-10 logarithm. If x is negative, these functions return an indefinite (IND), by default. If x is 0, they return infinity (INF).

Input SEH exception _matherr exception
± QNaN, IND none _DOMAIN

log and log10 have an implementation that uses Streaming SIMD Extensions 2 (SSE2). See _set_SSE2_enable for information and restrictions on using the SSE2 implementation.


C++ allows overloading, so you can call overloads of log and log10 that take and return float or long double values. In a C program, unless you're using the <tgmath.h> macro to call this function, log and log10 always take and return a double.

If you use the <tgmath.h> log() macro, the type of the argument determines which version of the function is selected. See Type-generic math for details.

By default, this function's global state is scoped to the application. To change this behavior, see Global state in the CRT.


Routine Required header
log, logf, logl, log10, log10f, log10l <math.h>
log macro <tgmath.h>

For more compatibility information, see Compatibility.


// crt_log.c
/* This program uses log and log10
* to calculate the natural logarithm and
* the base-10 logarithm of 9,000.

#include <math.h>
#include <stdio.h>

int main( void )
   double x = 9000.0;
   double y;

   y = log( x );
   printf( "log( %.2f ) = %f\n", x, y );
   y = log10( x );
   printf( "log10( %.2f ) = %f\n", x, y );
log( 9000.00 ) = 9.104980
log10( 9000.00 ) = 3.954243

To generate logarithms for other bases, use the mathematical relation: log base b of a == natural log (a) / natural log (b).

// logbase.cpp
#include <math.h>
#include <stdio.h>

double logbase(double a, double base)
   return log(a) / log(base);

int main()
   double x = 65536;
   double result;

   result = logbase(x, 2);
   printf("Log base 2 of %lf is %lf\n", x, result);
Log base 2 of 65536.000000 is 16.000000

See also

Math and floating-point support
exp, expf, expl
pow, powf, powl