# LOG (Transact-SQL)

**Applies to:**
SQL Server
Azure SQL Database
Azure SQL Managed Instance
Azure Synapse Analytics
Analytics Platform System (PDW)
SQL analytics endpoint in Microsoft Fabric
Warehouse in Microsoft Fabric

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 (12.x) and earlier versions, 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)

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