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LOG (Transact-SQL)

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

Applies to: SQL Server (SQL Server 2008 through current version), Azure SQL Database.

Topic link icon Transact-SQL Syntax Conventions

-- SQL Server Syntax
LOG ( float_expression [, base ] )
-- Windows Azure SQL Database Syntax
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 through SQL Server 2014.

By default, LOG() returns the natural logarithm. Starting with SQL Server 2012, 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.

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)
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