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

-- Syntax for Azure Synapse SQL 
  
LOG ( float_expression )  

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

float

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.

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's the result set.

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

The following example calculates the LOG for the exponent of a number.

SELECT LOG (EXP (10));  
  

Here's the result set.

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

The following example calculates the LOG for the specified float expression.

SELECT LOG(10);  

Here's the result set.

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

Mathematical Functions (Transact-SQL)
EXP (Transact-SQL)
LOG10 (Transact-SQL)