> For the complete documentation index, see [llms.txt](https://math-5.gitbook.io/math/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://math-5.gitbook.io/math/reference/mathematical-operations/log.md).

# log

## Find the logarithm of argument x with the base of a

```cpp
log<return_type>(a, x);
```

will return the logarithm of the argument x with the base a, both given as arguments. The return\_type specifies in which data type the result will be returned in, like shown in below example:&#x20;

```cpp
log<int>(20, 400); //2
log<float>(1.43, 543.18); //17.6066
```

{% hint style="danger" %}
Just like ln(x), log(a, x) isn't defined for all non-positive arguments x, as the compiler will throw an exception:

```
Error: Logarithm is undefined for non-positive values.
```

{% endhint %}

Because the ln(x) function is so precise,  we can just use the:&#x20;

$$
log\_a(x) = \frac{ln(x)}{ln(a)}
$$

formula to calculate the given logarithm.&#x20;