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# PostgreSQL LOG() Function

**Summary**: in this tutorial, you will learn how to use the PostgreSQL `LOG()` function to calculate the logarithm of a number

## Introduction to the PostgreSQL LOG() function

In PostgreSQL, the `LOG()` function allows you to calculate the logarithm of a number. PostgreSQL offers two `LOG()` functions:

Base-10 logarithm: The base-10 logarithm is the most commonly used logarithm in science and engineering applications.

Here's the syntax of the `LOG()` function that calculates the base-10 logarithm of a number:

```sql
LOG(n)
```

In this syntax:

- `n` is a number with the type [numeric](../postgresql-tutorial/postgresql-numeric) or [double precision](../postgresql-tutorial/postgresql-double-precision-type) you want to calculate the base-10 logarithm.

The `LOG()` function returns the base-10 logarithm with the same type as the type of the input number (`n`), which is `numeric` and `double precision` respectively. If n is `NULL` the `LOG()` function returns `NULL`.

If `n` is a text string, the `LOG()` function will attempt to convert it into a number before calculating the logarithm. It raises an error if the conversion fails.

The second `LOG()` function allows you to calculate the logarithm of a number with a specified base:

```sql
LOG(b, n)
```

In this syntax:

- `b` is the base of the logarithm. `b` can be a value of the [numeric](../postgresql-tutorial/postgresql-numeric) type.
- `n` has the same meaning in the `LOG(n)` function.

To calculate the natural logarithm of a number, you use the `LN()` function instead.

## PostgreSQL LOG() function examples

Let's take some examples of using the `LOG()` function.

### 1) Basic PostgreSQL LOG() function examples

The following example uses the `LOG()` function to calculate the base-10 logarithm of `100`:

```sql
SELECT LOG(100);
```

Output:

```text
 log
-----
   2
```

The following statement uses the second form of the `LOG()` function to calculate the base-10 logarithm of 100:

```sql
SELECT LOG(10,100);
```

Output:

```text
        log
--------------------
 2.0000000000000000
```

The following statement uses the `LOG()` function to calculate the base-2 logarithm of 8:

```sql
SELECT LOG(2,8);
```

Output:

```text
        log
--------------------
 3.0000000000000000
```

### 2) Using LOG() function with text

The following statement uses the `LOG()` function to calculate the base-2 logarithm of the text `'64'`:

```sql
SELECT LOG(2, '64');
```

Output:

```text
        log
--------------------
 6.0000000000000000
(1 row)
```

In this example, the `LOG()` function converts the text `'64'` into a number and calculate the base-2 logarithm of 64.

The following example raises an error because the `LOG()` function cannot convert the string `'64x'` into a number for calculation:

```sql
SELECT LOG('64x');
```

Error:

```
ERROR:  invalid input syntax for type double precision: "64x"
LINE 1: SELECT LOG('64x');                  ^
```

## Summary

- Use `LOG(n)` function to calculate the base-10 logarithm of the number `n`.
- Use `LOG(b, n)` function to calculate the logarithm of the number `n` with the base `b`.

---

## Related docs (Math Functions)

- [ABS](https://neon.com/postgresql/postgresql-math-functions/postgresql-abs)
- [CBRT](https://neon.com/postgresql/postgresql-math-functions/postgresql-cbrt)
- [CEIL](https://neon.com/postgresql/postgresql-math-functions/postgresql-ceil)
- [DEGREES](https://neon.com/postgresql/postgresql-math-functions/postgresql-degrees)
- [DIV](https://neon.com/postgresql/postgresql-math-functions/postgresql-div)
- [EXP](https://neon.com/postgresql/postgresql-math-functions/postgresql-exp)
- [FACTORIAL](https://neon.com/postgresql/postgresql-math-functions/postgresql-factorial)
- [FLOOR](https://neon.com/postgresql/postgresql-math-functions/postgresql-floor)
- [GCD](https://neon.com/postgresql/postgresql-math-functions/postgresql-gcd)
- [LCM](https://neon.com/postgresql/postgresql-math-functions/postgresql-lcm)
- [LN](https://neon.com/postgresql/postgresql-math-functions/postgresql-ln)
- [MOD](https://neon.com/postgresql/postgresql-math-functions/postgresql-mod)
- [MIN_SCALE](https://neon.com/postgresql/postgresql-math-functions/postgresql-min_scale)
- [PI](https://neon.com/postgresql/postgresql-math-functions/postgresql-pi-function)
- [POWER](https://neon.com/postgresql/postgresql-math-functions/postgresql-power)
- [RADIANS](https://neon.com/postgresql/postgresql-math-functions/postgresql-radians)
- [RANDOM](https://neon.com/postgresql/postgresql-math-functions/postgresql-random)
- [ROUND](https://neon.com/postgresql/postgresql-math-functions/postgresql-round)
- [SCALE](https://neon.com/postgresql/postgresql-math-functions/postgresql-scale)
- [SIGN](https://neon.com/postgresql/postgresql-math-functions/postgresql-sign)
- [SQRT](https://neon.com/postgresql/postgresql-math-functions/postgresql-sqrt)
- [TRIM_SCALE](https://neon.com/postgresql/postgresql-math-functions/postgresql-trim_scale)
- [TRUNC](https://neon.com/postgresql/postgresql-math-functions/postgresql-trunc)
- [WIDTH_BUCKET](https://neon.com/postgresql/postgresql-math-functions/postgresql-width_bucket)