LOG (Transact-SQL)

Applies to: yesSQL Server (all supported versions) YesAzure SQL Database YesAzure SQL Managed Instance yesAzure Synapse Analytics yesParallel Data Warehouse

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

Topic link icon 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 (SQL Data Warehouse) and Parallel Data Warehouse

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)