C log() Function

The log() function in C is a standard library function that computes the natural logarithm (base ( e )) of a given number. It is part of the C standard library (math.h). This function is useful for performing logarithmic calculations.

Table of Contents

1. Introduction
2. log() Function Syntax
3. Understanding log() Function
4. Examples
   • Computing the Natural Logarithm of a Value
   • Using log() with User Input
5. Real-World Use Case
6. Conclusion

Introduction

The log() function calculates the natural logarithm of a given number ( x ). The natural logarithm is the logarithm to the base ( e ) (approximately 2.71828) and is widely used in mathematics, physics, and engineering.

log() Function Syntax

The syntax for the log() function is as follows:

#include <math.h>
double log(double x);

Parameters:

• x: The value for which the natural logarithm is to be computed. The value must be positive.

Returns:

• The function returns the natural logarithm of the value x.

Understanding log() Function

The log() function takes a positive value ( x ) as input and returns the natural logarithm of that value. If the input value is negative or zero, the function will return a domain error.

Examples

Computing the Natural Logarithm of a Value

To demonstrate how to use log() to compute the natural logarithm of a value, we will write a simple program.

Example

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

int main() {
    double value = 2.71828;

    // Compute the natural logarithm of the value
    double natural_log = log(value);

    // Print the result
    printf("Natural logarithm of %.5f is: %.5f\n", value, natural_log);

    return 0;
}

Output:

Natural logarithm of 2.71828 is: 1.00000

Using log() with User Input

This example shows how to use log() to compute the natural logarithm of a value provided by the user.

Example

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

int main() {
    double value;

    // Get user input for the value
    printf("Enter a positive value: ");
    scanf("%lf", &value);

    // Check if the input value is valid
    if (value <= 0) {
        printf("Invalid input! Please enter a positive value.\n");
        return 1;
    }

    // Compute the natural logarithm of the value
    double natural_log = log(value);

    // Print the result
    printf("Natural logarithm of %.5f is: %.5f\n", value, natural_log);

    return 0;
}

Output (example user input "2.71828"):

Enter a positive value: 2.71828
Natural logarithm of 2.71828 is: 1.00000

Real-World Use Case

Calculating Compound Interest

In real-world applications, the log() function can be used to calculate the time required to reach a certain amount with continuous compounding interest.

Example: Calculating Time for Continuous Compounding

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

int main() {
    double principal, amount, rate, time;

    // Get user input for the principal amount, desired amount, and interest rate
    printf("Enter the principal amount: ");
    scanf("%lf", &principal);
    printf("Enter the desired amount: ");
    scanf("%lf", &amount);
    printf("Enter the annual interest rate (in decimal): ");
    scanf("%lf", &rate);

    // Check if the input values are valid
    if (principal <= 0 || amount <= 0 || rate <= 0) {
        printf("Invalid input! All values must be positive.\n");
        return 1;
    }

    // Calculate the time required using the natural logarithm
    time = log(amount / principal) / rate;

    // Print the result
    printf("Time required to reach %.2f from %.2f at an annual interest rate of %.2f is: %.2f years\n", amount, principal, rate, time);

    return 0;
}

Output (example user input principal "1000", amount "2000", rate "0.05"):

Enter the principal amount: 1000
Enter the desired amount: 2000
Enter the annual interest rate (in decimal): 0.05
Time required to reach 2000.00 from 1000.00 at an annual interest rate of 0.05 is: 13.86 years

Conclusion

The log() function is essential for computing the natural logarithm of a value in C. It is useful in various mathematical calculations, particularly in fields like mathematics, physics, and engineering, where logarithmic functions are required.