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Math.Log Method (Double, Double)

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

Namespace:  System
Assemblies:   mscorlib (in mscorlib.dll)
  System.Runtime.Extensions (in System.Runtime.Extensions.dll)

public static double Log(
	double a,
	double newBase
)

Parameters

a
Type: System.Double

The number whose logarithm is to be found.

newBase
Type: System.Double

The base of the logarithm.

Return Value

Type: System.Double
One of the values in the following table. (+Infinity denotes PositiveInfinity, -Infinity denotes NegativeInfinity, and NaN denotes NaN.)

a

newBase

Return value

a > 0

(0 < newBase < 1) -or-(newBase > 1)

lognewBase(a)

a < 0

(any value)

NaN

(any value)

newBase < 0

NaN

a != 1

newBase = 0

NaN

a != 1

newBase = +Infinity

NaN

a = NaN

(any value)

NaN

(any value)

newBase = NaN

NaN

(any value)

newBase = 1

NaN

a = 0

0 < newBase < 1

+Infinity

a = 0

newBase > 1

-Infinity

a = +Infinity

0 < newBase < 1

-Infinity

a = +Infinity

newBase > 1

+Infinity

a = 1

newBase = 0

0

a = 1

newBase = +Infinity

0

The following example uses Log to evaluate certain logarithmic identities for selected values.

// Example for the Math.Log( double ) and Math.Log( double, double ) methods. 
using System;

class LogDLogDD
{
    public static void Main() 
    {
        Console.WriteLine( 
            "This example of Math.Log( double ) and " +
            "Math.Log( double, double )\n" +
            "generates the following output.\n" );
        Console.WriteLine( 
            "Evaluate these identities with " +
            "selected values for X and B (base):" );
        Console.WriteLine( "   log(B)[X] == 1 / log(X)[B]" );
        Console.WriteLine( "   log(B)[X] == ln[X] / ln[B]" );
        Console.WriteLine( "   log(B)[X] == log(B)[e] * ln[X]" );

        UseBaseAndArg(0.1, 1.2);
        UseBaseAndArg(1.2, 4.9);
        UseBaseAndArg(4.9, 9.9);
        UseBaseAndArg(9.9, 0.1);
    }

    // Evaluate logarithmic identities that are functions of two arguments. 
    static void UseBaseAndArg(double argB, double argX)
    {
        // Evaluate log(B)[X] == 1 / log(X)[B].
        Console.WriteLine( 
            "\n                   Math.Log({1}, {0}) == {2:E16}" + 
            "\n             1.0 / Math.Log({0}, {1}) == {3:E16}", 
            argB, argX, Math.Log(argX, argB),
            1.0 / Math.Log(argB, argX) );

        // Evaluate log(B)[X] == ln[X] / ln[B].
        Console.WriteLine( 
            "        Math.Log({1}) / Math.Log({0}) == {2:E16}",
            argB, argX, Math.Log(argX) / Math.Log(argB) );

        // Evaluate log(B)[X] == log(B)[e] * ln[X].
        Console.WriteLine( 
            "Math.Log(Math.E, {0}) * Math.Log({1}) == {2:E16}", 
            argB, argX, Math.Log(Math.E, argB) * Math.Log(argX) );
    }
}

/*
This example of Math.Log( double ) and Math.Log( double, double )
generates the following output.

Evaluate these identities with selected values for X and B (base):
   log(B)[X] == 1 / log(X)[B]
   log(B)[X] == ln[X] / ln[B]
   log(B)[X] == log(B)[e] * ln[X]

                   Math.Log(1.2, 0.1) == -7.9181246047624818E-002
             1.0 / Math.Log(0.1, 1.2) == -7.9181246047624818E-002
        Math.Log(1.2) / Math.Log(0.1) == -7.9181246047624818E-002
Math.Log(Math.E, 0.1) * Math.Log(1.2) == -7.9181246047624804E-002

                   Math.Log(4.9, 1.2) == 8.7166610085093179E+000
             1.0 / Math.Log(1.2, 4.9) == 8.7166610085093161E+000
        Math.Log(4.9) / Math.Log(1.2) == 8.7166610085093179E+000
Math.Log(Math.E, 1.2) * Math.Log(4.9) == 8.7166610085093179E+000

                   Math.Log(9.9, 4.9) == 1.4425396251981288E+000
             1.0 / Math.Log(4.9, 9.9) == 1.4425396251981288E+000
        Math.Log(9.9) / Math.Log(4.9) == 1.4425396251981288E+000
Math.Log(Math.E, 4.9) * Math.Log(9.9) == 1.4425396251981288E+000

                   Math.Log(0.1, 9.9) == -1.0043839404494075E+000
             1.0 / Math.Log(9.9, 0.1) == -1.0043839404494075E+000
        Math.Log(0.1) / Math.Log(9.9) == -1.0043839404494075E+000
Math.Log(Math.E, 9.9) * Math.Log(0.1) == -1.0043839404494077E+000
*/

.NET Framework

Supported in: 4.6, 4.5, 4, 3.5, 3.0, 2.0, 1.1

.NET Framework Client Profile

Supported in: 4, 3.5 SP1

.NET for Windows Phone apps

Supported in: Windows Phone 8.1, Windows Phone Silverlight 8.1, Windows Phone Silverlight 8

Portable Class Library

Supported in: Portable Class Library
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