# BigInteger.Log Method

## Definition

Returns the logarithm of a specified number.

 Log(BigInteger) Returns the natural (base `e`) logarithm of a specified number. Log(BigInteger, Double) Returns the logarithm of a specified number in a specified base.

## Log(BigInteger)

Returns the natural (base `e`) logarithm of a specified number.

``````public:
static double Log(System::Numerics::BigInteger value);``````
``public static double Log (System.Numerics.BigInteger value);``
``static member Log : System.Numerics.BigInteger -> double``
``Public Shared Function Log (value As BigInteger) As Double``

#### Parameters

value
BigInteger

The number whose logarithm is to be found.

#### Returns

Double

The natural (base `e`) logarithm of `value`, as shown in the table in the Remarks section.

#### Exceptions

The natural log of `value` is out of range of the Double data type.

### Remarks

The `value` parameter is specified as a base 10 number.

The precise return value of this method depends on the sign of `value`, as the following table shows.

Sign of `value` parameter Return value
Positive The natural logarithm of `value`; that is, ln `value`, or log e`value`.
Zero NegativeInfinity.
Negative NaN.

To calculate the base 10 logarithm of a BigInteger value, call the Log10 method. To calculate the logarithm of a number in another base, call the Log(BigInteger, Double) method.

You can find the square root of a number by calling the Log method along with the Math.Exp method. Note that the result is Double.PositiveInfinity if the result is greater than Double.MaxValue. The following example calculates the square root of each element in an array of BigInteger values.

``````using System;
using System.Numerics;

public class Example
{
public static void Main()
{
BigInteger[] values = { 2, 100, BigInteger.Pow(1000, 100),
BigInteger.Pow(2, 64) };
foreach (var value in values)
Console.WriteLine("The square root of {0} is {1}", value,
Math.Exp(BigInteger.Log(value) / 2));
}
}
// The example displays the following output:
//    The square root of 2 is 1.41421356237309
//    The square root of 100 is 10
//    The square root of 1000000000000000000000000000000000000000000000000000000000000
//    00000000000000000000000000000000000000000000000000000000000000000000000000000000
//    00000000000000000000000000000000000000000000000000000000000000000000000000000000
//    00000000000000000000000000000000000000000000000000000000000000000000000000000000
//     is 9.99999999999988E+149
//    The square root of 18446744073709551616 is 4294967296
``````
``````Imports System.Numerics

Module Example
Public Sub Main()
Dim values() As BigInteger = { 2, 100, BigInteger.Pow(1000, 100),
BigInteger.Pow(2, 64) }
For Each value In values
Console.WriteLine("The square root of {0} is {1}", value,
Math.Exp(BigInteger.Log(value) / 2))
Next
End Sub
End Module
' The example displays the following output:
'    The square root of 2 is 1.41421356237309
'    The square root of 100 is 10
'    The square root of 1000000000000000000000000000000000000000000000000000000000000
'    00000000000000000000000000000000000000000000000000000000000000000000000000000000
'    00000000000000000000000000000000000000000000000000000000000000000000000000000000
'    00000000000000000000000000000000000000000000000000000000000000000000000000000000
'     is 9.99999999999988E+149
'    The square root of 18446744073709551616 is 4294967296
``````

This method corresponds to the Math.Log(Double) method for the primitive numeric types.

## Log(BigInteger, Double)

Returns the logarithm of a specified number in a specified base.

``````public:
static double Log(System::Numerics::BigInteger value, double baseValue);``````
``public static double Log (System.Numerics.BigInteger value, double baseValue);``
``static member Log : System.Numerics.BigInteger * double -> double``
``Public Shared Function Log (value As BigInteger, baseValue As Double) As Double``

#### Parameters

value
BigInteger

A number whose logarithm is to be found.

baseValue
Double

The base of the logarithm.

#### Returns

Double

The base `baseValue` logarithm of `value`, as shown in the table in the Remarks section.

#### Exceptions

The log of `value` is out of range of the Double data type.

### Remarks

The `value` and `baseValue` parameters are specified as base 10 numbers.

The precise return value of the method depends on the sign of `value` and on the sign and value of `baseValue`, as the following table shows.

`value` parameter `baseValue` parameter Return value
`value` > 0 (0 < `baseValue` < 1) -or-(`baseValue` > 1) logbaseValue(`value`)
`value` < 0 (any value) Double.NaN
(any value) `baseValue` < 0 Double.NaN
`value` != 1 `baseValue` = 0 Double.NaN
`value` != 1 `baseValue` = Double.PositiveInfinity Double.NaN
(any value) `baseValue` = Double.NaN Double.NaN
(any value) `baseValue` = 1 Double.NaN
`value` = 0 0 < `baseValue` < 1 Double.PositiveInfinity
`value` = 0 `baseValue` > 1 Double.PositiveInfinity
`value` = 1 `baseValue` = 0 0
`value` = 1 `baseValue` = Double.PositiveInfinity 0

To calculate the base 10 logarithm of a BigInteger value, call the Log10 method. To calculate the natural logarithm of a number, call the Log(BigInteger) method.

This method corresponds to the Math.Log method for the primitive numeric types.