Math.Exp-Methode

Gibt die angegebene Potenz von e zurück.

Namespace: System
Assembly: mscorlib (in mscorlib.dll)

Syntax

'Declaration
Public Shared Function Exp ( _
    d As Double _
) As Double
'Usage
Dim d As Double
Dim returnValue As Double

returnValue = Math.Exp(d)

public static double Exp (
    double d
)

public:
static double Exp (
    double d
)

public static double Exp (
    double d
)

public static function Exp (
    d : double
) : double

Parameter

• d
  Eine Zahl, die einen Exponenten darstellt.

Rückgabewert

Die Zahl e hoch d. Wenn d gleich NaN oder PositiveInfinity ist, wird dieser Wert zurückgegeben. Wenn d gleich NegativeInfinity ist, wird 0 zurückgegeben.

Hinweise

Mit der Pow-Methode können Potenzen von anderen Basen berechnet werden.

Exp ist die Umkehrfunktion von Log.

Beispiel

Im folgenden Beispiel werden mit Exp bestimmte exponentielle und logarithmische Identitäten für ausgewählte Werte ausgewertet.

' Example for the Math.Exp( Double ) method.
Imports System
Imports Microsoft.VisualBasic

Module ExpDemo
   
    Sub Main()
        Console.WriteLine( _
            "This example of Math.Exp( Double ) " & _
            "generates the following output." & vbCrLf)
        Console.WriteLine( _
            "Evaluate [e ^ ln(X) == ln(e ^ X) == X] " & _
            "with selected values for X:")

        UseLnExp(0.1)
        UseLnExp(1.2)
        UseLnExp(4.9)
        UseLnExp(9.9)
          
        Console.WriteLine( vbCrLf & _
            "Evaluate these identities with selected values for X and Y:")
        Console.WriteLine("   (e ^ X) * (e ^ Y) = e ^ (X + Y)")
        Console.WriteLine("   (e ^ X) ^ Y = e ^ (X * Y)")
        Console.WriteLine("   X ^ Y = e ^ (Y * ln(X))")
          
        UseTwoArgs(0.1, 1.2)
        UseTwoArgs(1.2, 4.9)
        UseTwoArgs(4.9, 9.9)
    End Sub 'Main
       
    ' Evaluate logarithmic/exponential identity with a given argument.
    Sub UseLnExp(arg As Double)

        ' Evaluate e ^ ln(X) = ln(e ^ X) = X.
        Console.WriteLine( _
            vbCrLf & "      Math.Exp(Math.Log({0})) = {1:E16}" + _
            vbCrLf & "      Math.Log(Math.Exp({0})) = {2:E16}", _
            arg, Math.Exp(Math.Log(arg)), Math.Log(Math.Exp(arg)))
    End Sub 'UseLnExp
       
    ' Evaluate exponential identities that are functions of two arguments.
    Sub UseTwoArgs(argX As Double, argY As Double)

        ' Evaluate (e ^ X) * (e ^ Y) = e ^ (X + Y).
        Console.WriteLine( _
            vbCrLf & "Math.Exp({0}) * Math.Exp({1}) = {2:E16}" + _
            vbCrLf & "          Math.Exp({0} + {1}) = {3:E16}", _
            argX, argY, Math.Exp(argX) * Math.Exp(argY), _
            Math.Exp((argX + argY)))
          
        ' Evaluate (e ^ X) ^ Y = e ^ (X * Y).
        Console.WriteLine( _
            " Math.Pow(Math.Exp({0}), {1}) = {2:E16}" + _
            vbCrLf & "          Math.Exp({0} * {1}) = {3:E16}", _
            argX, argY, Math.Pow(Math.Exp(argX), argY), _
            Math.Exp((argX * argY)))
          
        ' Evaluate X ^ Y = e ^ (Y * ln(X)).
        Console.WriteLine( _
            "           Math.Pow({0}, {1}) = {2:E16}" + _
            vbCrLf & "Math.Exp({1} * Math.Log({0})) = {3:E16}", _
            argX, argY, Math.Pow(argX, argY), _
            Math.Exp((argY * Math.Log(argX))))

    End Sub 'UseTwoArgs
End Module 'ExpDemo

' This example of Math.Exp( Double ) generates the following output.
' 
' Evaluate [e ^ ln(X) == ln(e ^ X) == X] with selected values for X:
' 
'       Math.Exp(Math.Log(0.1)) = 1.0000000000000001E-001
'       Math.Log(Math.Exp(0.1)) = 1.0000000000000008E-001
' 
'       Math.Exp(Math.Log(1.2)) = 1.2000000000000000E+000
'       Math.Log(Math.Exp(1.2)) = 1.2000000000000000E+000
' 
'       Math.Exp(Math.Log(4.9)) = 4.9000000000000012E+000
'       Math.Log(Math.Exp(4.9)) = 4.9000000000000004E+000
' 
'       Math.Exp(Math.Log(9.9)) = 9.9000000000000004E+000
'       Math.Log(Math.Exp(9.9)) = 9.9000000000000004E+000
' 
' Evaluate these identities with selected values for X and Y:
'    (e ^ X) * (e ^ Y) = e ^ (X + Y)
'    (e ^ X) ^ Y = e ^ (X * Y)
'    X ^ Y = e ^ (Y * ln(X))
' 
' Math.Exp(0.1) * Math.Exp(1.2) = 3.6692966676192444E+000
'           Math.Exp(0.1 + 1.2) = 3.6692966676192444E+000
'  Math.Pow(Math.Exp(0.1), 1.2) = 1.1274968515793757E+000
'           Math.Exp(0.1 * 1.2) = 1.1274968515793757E+000
'            Math.Pow(0.1, 1.2) = 6.3095734448019331E-002
' Math.Exp(1.2 * Math.Log(0.1)) = 6.3095734448019344E-002
' 
' Math.Exp(1.2) * Math.Exp(4.9) = 4.4585777008251705E+002
'           Math.Exp(1.2 + 4.9) = 4.4585777008251716E+002
'  Math.Pow(Math.Exp(1.2), 4.9) = 3.5780924170885260E+002
'           Math.Exp(1.2 * 4.9) = 3.5780924170885277E+002
'            Math.Pow(1.2, 4.9) = 2.4433636334442981E+000
' Math.Exp(4.9 * Math.Log(1.2)) = 2.4433636334442981E+000
' 
' Math.Exp(4.9) * Math.Exp(9.9) = 2.6764450551890982E+006
'           Math.Exp(4.9 + 9.9) = 2.6764450551891015E+006
'  Math.Pow(Math.Exp(4.9), 9.9) = 1.1684908531676833E+021
'           Math.Exp(4.9 * 9.9) = 1.1684908531676829E+021
'            Math.Pow(4.9, 9.9) = 6.8067718210957060E+006
' Math.Exp(9.9 * Math.Log(4.9)) = 6.8067718210956985E+006

// Example for the Math.Exp( double ) method.
using System;

class ExpDemo 
{
    public static void Main() 
    {
        Console.WriteLine( 
            "This example of Math.Exp( double ) " +
            "generates the following output.\n" );
        Console.WriteLine( 
            "Evaluate [e ^ ln(X) == ln(e ^ X) == X] " +
            "with selected values for X:" );

        UseLnExp(0.1);
        UseLnExp(1.2);
        UseLnExp(4.9);
        UseLnExp(9.9);

        Console.WriteLine( 
            "\nEvaluate these identities with " +
            "selected values for X and Y:" );
        Console.WriteLine( "   (e ^ X) * (e ^ Y) == e ^ (X + Y)" );
        Console.WriteLine( "   (e ^ X) ^ Y == e ^ (X * Y)" );
        Console.WriteLine( "   X ^ Y == e ^ (Y * ln(X))" );

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

    // Evaluate logarithmic/exponential identity with a given argument.
    static void UseLnExp(double arg)
    {
        // Evaluate e ^ ln(X) == ln(e ^ X) == X.
        Console.WriteLine( 
            "\n      Math.Exp(Math.Log({0})) == {1:E16}\n" +
            "      Math.Log(Math.Exp({0})) == {2:E16}",
            arg, Math.Exp(Math.Log(arg)), Math.Log(Math.Exp(arg)) );
    }

    // Evaluate exponential identities that are functions of two arguments.
    static void UseTwoArgs(double argX, double argY)
    {
        // Evaluate (e ^ X) * (e ^ Y) == e ^ (X + Y).
        Console.WriteLine( 
            "\nMath.Exp({0}) * Math.Exp({1}) == {2:E16}" + 
            "\n          Math.Exp({0} + {1}) == {3:E16}", 
            argX, argY, Math.Exp(argX) * Math.Exp(argY),
            Math.Exp(argX + argY) );

        // Evaluate (e ^ X) ^ Y == e ^ (X * Y).
        Console.WriteLine( 
            " Math.Pow(Math.Exp({0}), {1}) == {2:E16}" +
            "\n          Math.Exp({0} * {1}) == {3:E16}",
            argX, argY, Math.Pow(Math.Exp(argX), argY),
            Math.Exp(argX * argY) );

        // Evaluate X ^ Y == e ^ (Y * ln(X)).
        Console.WriteLine( 
            "           Math.Pow({0}, {1}) == {2:E16}" + 
            "\nMath.Exp({1} * Math.Log({0})) == {3:E16}", 
            argX, argY, Math.Pow(argX, argY), 
            Math.Exp(argY * Math.Log(argX)) );
    }
}

/*
This example of Math.Exp( double ) generates the following output.

Evaluate [e ^ ln(X) == ln(e ^ X) == X] with selected values for X:

      Math.Exp(Math.Log(0.1)) == 1.0000000000000001E-001
      Math.Log(Math.Exp(0.1)) == 1.0000000000000008E-001

      Math.Exp(Math.Log(1.2)) == 1.2000000000000000E+000
      Math.Log(Math.Exp(1.2)) == 1.2000000000000000E+000

      Math.Exp(Math.Log(4.9)) == 4.9000000000000012E+000
      Math.Log(Math.Exp(4.9)) == 4.9000000000000004E+000

      Math.Exp(Math.Log(9.9)) == 9.9000000000000004E+000
      Math.Log(Math.Exp(9.9)) == 9.9000000000000004E+000

Evaluate these identities with selected values for X and Y:
   (e ^ X) * (e ^ Y) == e ^ (X + Y)
   (e ^ X) ^ Y == e ^ (X * Y)
   X ^ Y == e ^ (Y * ln(X))

Math.Exp(0.1) * Math.Exp(1.2) == 3.6692966676192444E+000
          Math.Exp(0.1 + 1.2) == 3.6692966676192444E+000
 Math.Pow(Math.Exp(0.1), 1.2) == 1.1274968515793757E+000
          Math.Exp(0.1 * 1.2) == 1.1274968515793757E+000
           Math.Pow(0.1, 1.2) == 6.3095734448019331E-002
Math.Exp(1.2 * Math.Log(0.1)) == 6.3095734448019344E-002

Math.Exp(1.2) * Math.Exp(4.9) == 4.4585777008251705E+002
          Math.Exp(1.2 + 4.9) == 4.4585777008251716E+002
 Math.Pow(Math.Exp(1.2), 4.9) == 3.5780924170885260E+002
          Math.Exp(1.2 * 4.9) == 3.5780924170885277E+002
           Math.Pow(1.2, 4.9) == 2.4433636334442981E+000
Math.Exp(4.9 * Math.Log(1.2)) == 2.4433636334442981E+000

Math.Exp(4.9) * Math.Exp(9.9) == 2.6764450551890982E+006
          Math.Exp(4.9 + 9.9) == 2.6764450551891015E+006
 Math.Pow(Math.Exp(4.9), 9.9) == 1.1684908531676833E+021
          Math.Exp(4.9 * 9.9) == 1.1684908531676829E+021
           Math.Pow(4.9, 9.9) == 6.8067718210957060E+006
Math.Exp(9.9 * Math.Log(4.9)) == 6.8067718210956985E+006
*/

// Example for the Math::Exp( double ) method.
using namespace System;

// Evaluate logarithmic/exponential identity with a given argument.
void UseLnExp( double arg )
{
   
   // Evaluate e ^ ln(X) == ln(e ^ X) == X.
   Console::WriteLine( "\n      Math::Exp(Math::Log({0})) == {1:E16}\n"
   "      Math::Log(Math::Exp({0})) == {2:E16}", arg, Math::Exp( Math::Log( arg ) ), Math::Log( Math::Exp( arg ) ) );
}


// Evaluate exponential identities that are functions of two arguments.
void UseTwoArgs( double argX, double argY )
{
   
   // Evaluate (e ^ X) * (e ^ Y) == e ^ (X + Y).
   Console::WriteLine( "\nMath::Exp({0}) * Math::Exp({1}) == {2:E16}"
   "\n           Math::Exp({0} + {1}) == {3:E16}", argX, argY, Math::Exp( argX ) * Math::Exp( argY ), Math::Exp( argX + argY ) );
   
   // Evaluate (e ^ X) ^ Y == e ^ (X * Y).
   Console::WriteLine( " Math::Pow(Math::Exp({0}), {1}) == {2:E16}"
   "\n           Math::Exp({0} * {1}) == {3:E16}", argX, argY, Math::Pow( Math::Exp( argX ), argY ), Math::Exp( argX * argY ) );
   
   // Evaluate X ^ Y == e ^ (Y * ln(X)).
   Console::WriteLine( "            Math::Pow({0}, {1}) == {2:E16}"
   "\nMath::Exp({1} * Math::Log({0})) == {3:E16}", argX, argY, Math::Pow( argX, argY ), Math::Exp( argY * Math::Log( argX ) ) );
}

int main()
{
   Console::WriteLine( "This example of Math::Exp( double ) "
   "generates the following output.\n" );
   Console::WriteLine( "Evaluate [e ^ ln(X) == ln(e ^ X) == X] "
   "with selected values for X:" );
   UseLnExp( 0.1 );
   UseLnExp( 1.2 );
   UseLnExp( 4.9 );
   UseLnExp( 9.9 );
   Console::WriteLine( "\nEvaluate these identities with "
   "selected values for X and Y:" );
   Console::WriteLine( "   (e ^ X) * (e ^ Y) == e ^ (X + Y)" );
   Console::WriteLine( "   (e ^ X) ^ Y == e ^ (X * Y)" );
   Console::WriteLine( "   X ^ Y == e ^ (Y * ln(X))" );
   UseTwoArgs( 0.1, 1.2 );
   UseTwoArgs( 1.2, 4.9 );
   UseTwoArgs( 4.9, 9.9 );
}

/*
This example of Math::Exp( double ) generates the following output.

Evaluate [e ^ ln(X) == ln(e ^ X) == X] with selected values for X:

      Math::Exp(Math::Log(0.1)) == 1.0000000000000001E-001
      Math::Log(Math::Exp(0.1)) == 1.0000000000000008E-001

      Math::Exp(Math::Log(1.2)) == 1.2000000000000000E+000
      Math::Log(Math::Exp(1.2)) == 1.2000000000000000E+000

      Math::Exp(Math::Log(4.9)) == 4.9000000000000012E+000
      Math::Log(Math::Exp(4.9)) == 4.9000000000000004E+000

      Math::Exp(Math::Log(9.9)) == 9.9000000000000004E+000
      Math::Log(Math::Exp(9.9)) == 9.9000000000000004E+000

Evaluate these identities with selected values for X and Y:
   (e ^ X) * (e ^ Y) == e ^ (X + Y)
   (e ^ X) ^ Y == e ^ (X * Y)
   X ^ Y == e ^ (Y * ln(X))

Math::Exp(0.1) * Math::Exp(1.2) == 3.6692966676192444E+000
           Math::Exp(0.1 + 1.2) == 3.6692966676192444E+000
 Math::Pow(Math::Exp(0.1), 1.2) == 1.1274968515793757E+000
           Math::Exp(0.1 * 1.2) == 1.1274968515793757E+000
            Math::Pow(0.1, 1.2) == 6.3095734448019331E-002
Math::Exp(1.2 * Math::Log(0.1)) == 6.3095734448019344E-002

Math::Exp(1.2) * Math::Exp(4.9) == 4.4585777008251705E+002
           Math::Exp(1.2 + 4.9) == 4.4585777008251716E+002
 Math::Pow(Math::Exp(1.2), 4.9) == 3.5780924170885260E+002
           Math::Exp(1.2 * 4.9) == 3.5780924170885277E+002
            Math::Pow(1.2, 4.9) == 2.4433636334442981E+000
Math::Exp(4.9 * Math::Log(1.2)) == 2.4433636334442981E+000

Math::Exp(4.9) * Math::Exp(9.9) == 2.6764450551890982E+006
           Math::Exp(4.9 + 9.9) == 2.6764450551891015E+006
 Math::Pow(Math::Exp(4.9), 9.9) == 1.1684908531676833E+021
           Math::Exp(4.9 * 9.9) == 1.1684908531676829E+021
            Math::Pow(4.9, 9.9) == 6.8067718210957060E+006
Math::Exp(9.9 * Math::Log(4.9)) == 6.8067718210956985E+006
*/

// Example for the Math.Exp( double ) method.
import System.*;

class ExpDemo
{
     public static void main(String[] args)
    {
        Console.WriteLine(("This example of Math.Exp( double ) " 
            + "generates the following output.\n"));
        Console.WriteLine(("Evaluate [e ^ ln(X) == ln(e ^ X) == X] " 
            + "with selected values for X:"));
        UseLnExp(0.1);
        UseLnExp(1.2);
        UseLnExp(4.9);
        UseLnExp(9.9);
        Console.WriteLine(("\nEvaluate these identities with " 
            + "selected values for X and Y:"));
        Console.WriteLine("   (e ^ X) * (e ^ Y) == e ^ (X + Y)");
        Console.WriteLine("   (e ^ X) ^ Y == e ^ (X * Y)");
        Console.WriteLine("   X ^ Y == e ^ (Y * ln(X))");
        UseTwoArgs(0.1, 1.2);
        UseTwoArgs(1.2, 4.9);
        UseTwoArgs(4.9, 9.9);
    } //main
   
    // Evaluate logarithmic/exponential identity with a given argument.
    static void UseLnExp(double arg) 
    {
        // Evaluate e ^ ln(X) == ln(e ^ X) == X.
        Console.WriteLine("\n     Math.Exp(Math.Log({0})) == {1}\n"
            + "     Math.Log(Math.Exp({0})) == {2}", 
            System.Convert.ToString(arg),
            ((System.Double)System.Math.Exp(
            System.Math.Log(arg))).ToString("E16"),
            ((System.Double)System.Math.Log(
            System.Math.Exp(arg))).ToString("E16"));
    } //UseLnExp
   
    // Evaluate exponential identities that are functions of two arguments.
    static void UseTwoArgs(double argX, double argY) 
    {
        // Evaluate (e ^ X) * (e ^ Y) == e ^ (X + Y).
        Console.WriteLine("\nMath.Exp({0}) * Math.Exp({1}) == {2}" 
            + "\n          Math.Exp({0} + {1}) == {3}",
            new Object[] {System.Convert.ToString(argX),
            System.Convert.ToString(argY),((System.Double )
            (System.Math.Exp(argX) * System.Math.Exp(argY))).ToString("E16"),
            ((System.Double )System.Math.Exp((argX + argY))).ToString("E16")});

        // Evaluate (e ^ X) ^ Y == e ^ (X * Y).
        Console.WriteLine(" Math.Pow(Math.Exp({0}), {1}) == {2}" 
            + "\n          Math.Exp({0} * {1}) == {3}",
            new Object[] { System.Convert.ToString(argX),
            System.Convert.ToString(argY),((System.Double)System.Math.Pow
            (System.Math.Exp(argX),argY)).ToString("E16"),
            ((System.Double)System.Math.Exp((argX * argY))).ToString("E16")});

        // Evaluate X ^ Y == e ^ (Y * ln(X)).
        Console.WriteLine("           Math.Pow({0}, {1}) == {2}" 
            + "\nMath.Exp({1} * Math.Log({0})) == {3}", 
            new Object[] { System.Convert.ToString(argX), 
            System.Convert.ToString(argY), 
            ((System.Double)System.Math.Pow(argX, argY)).ToString("E16"),
            ((System.Double)System.Math.Exp(
            (argY * System.Math.Log(argX)))).ToString("E16") });
    } //UseTwoArgs
} //ExpDemo

/*
This example of Math.Exp( double ) generates the following output.

Evaluate [e ^ ln(X) == ln(e ^ X) == X] with selected values for X:

      Math.Exp(Math.Log(0.1)) == 1.0000000000000001E-001
      Math.Log(Math.Exp(0.1)) == 1.0000000000000008E-001

      Math.Exp(Math.Log(1.2)) == 1.2000000000000000E+000
      Math.Log(Math.Exp(1.2)) == 1.2000000000000000E+000

      Math.Exp(Math.Log(4.9)) == 4.9000000000000012E+000
      Math.Log(Math.Exp(4.9)) == 4.9000000000000004E+000

      Math.Exp(Math.Log(9.9)) == 9.9000000000000004E+000
      Math.Log(Math.Exp(9.9)) == 9.9000000000000004E+000

Evaluate these identities with selected values for X and Y:
   (e ^ X) * (e ^ Y) == e ^ (X + Y)
   (e ^ X) ^ Y == e ^ (X * Y)
   X ^ Y == e ^ (Y * ln(X))

Math.Exp(0.1) * Math.Exp(1.2) == 3.6692966676192444E+000
          Math.Exp(0.1 + 1.2) == 3.6692966676192444E+000
 Math.Pow(Math.Exp(0.1), 1.2) == 1.1274968515793757E+000
          Math.Exp(0.1 * 1.2) == 1.1274968515793757E+000
           Math.Pow(0.1, 1.2) == 6.3095734448019331E-002
Math.Exp(1.2 * Math.Log(0.1)) == 6.3095734448019344E-002

Math.Exp(1.2) * Math.Exp(4.9) == 4.4585777008251705E+002
          Math.Exp(1.2 + 4.9) == 4.4585777008251716E+002
 Math.Pow(Math.Exp(1.2), 4.9) == 3.5780924170885260E+002
          Math.Exp(1.2 * 4.9) == 3.5780924170885277E+002
           Math.Pow(1.2, 4.9) == 2.4433636334442981E+000
Math.Exp(4.9 * Math.Log(1.2)) == 2.4433636334442981E+000

Math.Exp(4.9) * Math.Exp(9.9) == 2.6764450551890982E+006
          Math.Exp(4.9 + 9.9) == 2.6764450551891015E+006
 Math.Pow(Math.Exp(4.9), 9.9) == 1.1684908531676833E+021
          Math.Exp(4.9 * 9.9) == 1.1684908531676829E+021
           Math.Pow(4.9, 9.9) == 6.8067718210957060E+006
Math.Exp(9.9 * Math.Log(4.9)) == 6.8067718210956985E+006
*/

Plattformen

Windows 98, Windows 2000 SP4, Windows CE, Windows Millennium Edition, Windows Mobile für Pocket PC, Windows Mobile für Smartphone, Windows Server 2003, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP SP2, Windows XP Starter Edition

.NET Framework unterstützt nicht alle Versionen sämtlicher Plattformen. Eine Liste der unterstützten Versionen finden Sie unter Systemanforderungen.

Versionsinformationen

.NET Framework

Unterstützt in: 2.0, 1.1, 1.0

.NET Compact Framework

Unterstützt in: 2.0, 1.0

Siehe auch

Referenz

Math-Klasse
Math-Member
System-Namespace
E
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