# LOG (Transact-SQL)

**Applies to:**
SQL Server (all supported versions)
Azure SQL Database
Azure SQL Managed Instance
Azure Synapse Analytics
Analytics Platform System (PDW)

Returns the natural logarithm of the specified **float** expression in SQL Server.

Transact-SQL Syntax Conventions

## Syntax

```
-- Syntax for SQL Server, Azure SQL Database
LOG ( float_expression [, base ] )
```

```
-- Syntax for Azure Synapse SQL
LOG ( float_expression )
```

Note

To view Transact-SQL syntax for SQL Server 2014 and earlier, see Previous versions documentation.

## Arguments

*float_expression*

Is an expression of type **float** or of a type that can be implicitly converted to **float**.

*base*

Optional integer argument that sets the base for the logarithm.

**Applies to**: SQL Server 2012 (11.x) and later

## Return Types

**float**

## Remarks

By default, **LOG()** returns the natural logarithm. Starting with SQL Server 2012 (11.x), you can change the base of the logarithm to another value by using the optional *base* parameter.

The natural logarithm is the logarithm to the base **e**, where **e** is an irrational constant approximately equal to 2.718281828.

The natural logarithm of the exponential of a number is the number itself: LOG( EXP( *n* ) ) = *n*. And the exponential of the natural logarithm of a number is the number itself: EXP( LOG( *n* ) ) = *n*.

## Examples

### A. Calculating the logarithm for a number.

The following example calculates the `LOG`

for the specified **float** expression.

```
DECLARE @var FLOAT = 10;
SELECT 'The LOG of the variable is: ' + CONVERT(VARCHAR, LOG(@var));
GO
```

Here is the result set.

```
-------------------------------------
The LOG of the variable is: 2.30259
(1 row(s) affected)
```

### B. Calculating the logarithm of the exponent of a number.

The following example calculates the `LOG`

for the exponent of a number.

```
SELECT LOG (EXP (10));
```

Here is the result set.

```
----------------------------------
10
(1 row(s) affected)
```

## Examples: Azure Synapse Analytics and Analytics Platform System (PDW)

### C. Calculating the logarithm for a number

The following example calculates the `LOG`

for the specified **float** expression.

```
SELECT LOG(10);
```

Here is the result set.

```
----------------`
2.30
```

## See Also

Mathematical Functions (Transact-SQL)

EXP (Transact-SQL)

LOG10 (Transact-SQL)