# 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.