log() function in C programming is a mathematical function provided by the math.h header file and is used to calculate the natural logarithm (base(e)) of a given number passed as parameter. This function returns natural logarithm of x as double and works with double data types for other data types like float or long double, we can use logf() and logl(), respectively.

Syntax of log() in C

double log(double x);

Parameters of log()

The log(x) function takes a single parameter x, where:

• x: is a value of type double whose natural logarithm is to be computed and the value of x must be positive.

Return Value of log()

The log(x) function returns the logarithm of the given number x passed as a parameter. If the value of x is negative then it returns a domain error (NaN) because the logarithm of a negative number returns an imaginary number which is not valid.

Examples of log() Function in C

Input:
double x = 10.0

Output:
The logarithm of 10.0 is 2.302585

Example 1

The below program demonstrates how we can calculate the log of a given numbers using the log(x) function in C.

// C Program to calculate the logrithm of given numbers

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

// Function to calculate the log of a number
void calculate_log(double value)
{
    // Reset errno before calling log
    errno = 0;
    double result = log(value);

    // Handle negative numbers
    if (errno == EDOM) {
        printf("Domain error: log of %f is undefined.\n",
               value);
    }
    else {
        printf("The natural logarithm of %f is %f\n", value,
               result);
    }
}

int main()
{
    // Define the numbers whose log is required
    double value1 = 5.0;
    double value2 = 10.0;
    double value3 = 15.0;
    double value4 = 20.0;
    double value5 = -10.0;

    // Calculate and print the natural logarithm for each
    // value
    calculate_log(value1);
    calculate_log(value2);
    calculate_log(value3);
    calculate_log(value4);
    calculate_log(value5);

    return 0;
}

Output

The natural logarithm of 5.000000 is 1.609438
The natural logarithm of 10.000000 is 2.302585
The natural logarithm of 15.000000 is 2.708050
The natural logarithm of 20.000000 is 2.995732
ERROR!
Domain error: log of -10.000000 is undefined.

Time Complexity: O(1)
Auxiliary Space: O(1)

Explanation: In the above program, the errno global variable is used for error handling. Whenever a negative number is provided as an parameter to the log function the value of errno is set to EDOM which denotes domain error. Domain error occurs when an input argument is outside the domain of a mathematical function.

Example 2

The below program demonstrates how we can calculate the logarithm of different data types in C.

// C program to calculate the logarithm of different data types
#include <math.h>
#include <stdio.h>

int main()
{
    // Declare variables of different data types
    // double type variable
    double num1 = 2.0;
    // float type variable
    float num2 = 3.0;
    // long double type variable
    long double num3 = 4.0;

    // Calculate the natural logarithm for various data types variables
    double result1 = log(num1);
    
    float result2 = logf(num2);
    
    long double result3 = logl(num3);

    // Print the results
    printf("Natural logarithm of %.2f is %.2f\n", num1, result1);
    printf("Natural logarithm of %.2f is %.2f\n", num2, result2);
    printf("Natural logarithm of %.2Lf is %.2Lf\n", num3, result3);

    return 0;
}

Natural logarithm of 2.00 is 0.69
Natural logarithm of 3.00 is 1.10
Natural logarithm of 4.00 is 1.39

Time Complexity: O(1)
Auxiliary Space: O(1)