# C log()

## Example 1: Calculating Natural Logarithm

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

int main() {
double x = 2.0;
double result = log(x);

printf("The natural logarithm of %.2f is %.2f\n", x, result);

return 0;
}``````

Output:

``The natural logarithm of 2.00 is 0.69``

Explanation:

In this example, the program calculates the natural logarithm of the number `2.0 `using the `log()` function. The result is then printed. The natural logarithm of a number `x` (ln(x)) is the power to which the base `e` (approximately 2.71828) must be raised to obtain `x`. In this case, the natural logarithm of 2.0 is approximately 0.69.

## Example 2: Calculating Logarithm with a Custom Base

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

int main() {
double x = 8.0;
double base = 2.0;
double result = log(x) / log(base);

printf("The logarithm base %.2f of %.2f is %.2f\n", base, x, result);

return 0;
}``````

Output:

``The logarithm base 2.00 of 8.00 is 3.00``

Explanation 2:

In this example, the program calculates the logarithm of the number `8.0` with base `2.0` using the change of base formula. The `log()` function calculates the natural logarithm, so to find the logarithm with a different base, we divide the natural logarithm of the number by the natural logarithm of the desired base. In this case, the logarithm base 2 of 8 is 3.

## Example 3: Calculating Logarithm of Negative Number

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

int main() {
double x = -5.0;
double result = log(x);

printf("The natural logarithm of %.2f is %.2f\n", x, result);

return 0;
}``````

Output:

``The natural logarithm of -5.00 is NaN``

Explanation:

In this example, the program tries to calculate the natural logarithm of a negative number (-5.0). However, the natural logarithm is undefined for negative numbers and will result in a "`Not-a-Number`" (NaN) value. This is because the domain of the natural logarithm function is restricted to positive real numbers.

Keep in mind that the examples provided here are simple demonstrations of the `log()` function in C. When working with real applications, you should handle potential errors and edge cases more robustly.

### FAQ's

1. What is the log() function in C used for?

The `log()` function in C is used to calculate the natural logarithm (base e) of a given number. It is part of the math library and can be used for various mathematical and scientific calculations.

2. What is the syntax of the log() function in C?

The syntax of the log() function in C is:

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

Where `x` is the number for which you want to calculate the natural logarithm.

4. What does the log() function return?

The `log()` function returns a `double` value, which is the natural logarithm of the input number `x`.

5. Can the log() function handle negative numbers or zero?

The `log()` function can handle positive numbers, but it is not defined for negative numbers or zero. Attempting to calculate the natural logarithm of a negative number or zero will result in undefined behavior.

8. Can the log() function handle very large or very small numbers?

The `log()` function can handle a wide range of input values, including very large and very small positive numbers, as long as they are within the limits of the `double` data type.