Math.Exp Method

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Returns e raised to the specified power.

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

Syntax

'Declaration
<SecuritySafeCriticalAttribute> _
Public Shared Function Exp ( _
    d As Double _
) As Double

[SecuritySafeCriticalAttribute]
public static double Exp(
    double d
)

Parameters

• d
  Type: System.Double
  A number specifying a power.

Return Value

Type: System.Double
The number e raised to the power d. If d equals NaN or PositiveInfinity, that value is returned. If d equals NegativeInfinity, 0 is returned.

Remarks

Use the Pow method to calculate powers of other bases.

Exp is the inverse of Log.

Examples

The following example uses Exp to evaluate certain exponential and logarithmic identities for selected values.

' Example for the Math.Exp( Double ) method.

Module Example

   Public Sub Demo(ByVal outputBlock As System.Windows.Controls.TextBlock)
      outputBlock.Text &= _
          "This example of Math.Exp( Double ) " & _
          "generates the following output." & vbCrLf & vbCrLf
      outputBlock.Text &= _
          "Evaluate [e ^ ln(X) == ln(e ^ X) == X] " & _
          "with selected values for X:" & vbCrLf

      UseLnExp(outputBlock, 0.1)
      UseLnExp(outputBlock, 1.2)
      UseLnExp(outputBlock, 4.9)
      UseLnExp(outputBlock, 9.9)

      outputBlock.Text &= vbCrLf & _
          "Evaluate these identities with selected values for X and Y:" & vbCrLf
      outputBlock.Text &= "   (e ^ X) * (e ^ Y) = e ^ (X + Y)" & vbCrLf
      outputBlock.Text &= "   (e ^ X) ^ Y = e ^ (X * Y)" & vbCrLf
      outputBlock.Text &= "   X ^ Y = e ^ (Y * ln(X))" & vbCrLf

      UseTwoArgs(outputBlock, 0.1, 1.2)
      UseTwoArgs(outputBlock, 1.2, 4.9)
      UseTwoArgs(outputBlock, 4.9, 9.9)
   End Sub 'Main

   ' Evaluate logarithmic/exponential identity with a given argument.
   Sub UseLnExp(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal arg As Double)

      ' Evaluate e ^ ln(X) = ln(e ^ X) = X.
      outputBlock.Text &= String.Format( _
          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))) & vbCrLf
   End Sub 'UseLnExp

   ' Evaluate exponential identities that are functions of two arguments.
   Sub UseTwoArgs(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal argX As Double, ByVal argY As Double)

      ' Evaluate (e ^ X) * (e ^ Y) = e ^ (X + Y).
      outputBlock.Text &= String.Format( _
          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))) & vbCrLf

      ' Evaluate (e ^ X) ^ Y = e ^ (X * Y).
      outputBlock.Text &= String.Format( _
          " 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))) & vbCrLf

      ' Evaluate X ^ Y = e ^ (Y * ln(X)).
      outputBlock.Text &= String.Format( _
          "           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)))) & vbCrLf

   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 Example
{
   public static void Demo(System.Windows.Controls.TextBlock outputBlock)
   {
      outputBlock.Text +=
          "This example of Math.Exp( double ) " +
          "generates the following output.\n" + "\n";
      outputBlock.Text +=
          "Evaluate [e ^ ln(X) == ln(e ^ X) == X] " +
          "with selected values for X:" + "\n";

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

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

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

   // Evaluate logarithmic/exponential identity with a given argument.
   static void UseLnExp(System.Windows.Controls.TextBlock outputBlock, double arg)
   {
      // Evaluate e ^ ln(X) == ln(e ^ X) == X.
      outputBlock.Text += String.Format(
          "\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))) + "\n";
   }

   // Evaluate exponential identities that are functions of two arguments.
   static void UseTwoArgs(System.Windows.Controls.TextBlock outputBlock, double argX, double argY)
   {
      // Evaluate (e ^ X) * (e ^ Y) == e ^ (X + Y).
      outputBlock.Text += String.Format(
          "\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)) + "\n";

      // Evaluate (e ^ X) ^ Y == e ^ (X * Y).
      outputBlock.Text += String.Format(
          " 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)) + "\n";

      // Evaluate X ^ Y == e ^ (Y * ln(X)).
      outputBlock.Text += String.Format(
          "           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))) + "\n";
   }
}

/*
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
*/

Version Information

Silverlight

Supported in: 5, 4, 3

Silverlight for Windows Phone

Supported in: Windows Phone OS 7.1, Windows Phone OS 7.0

XNA Framework

Supported in: Xbox 360, Windows Phone OS 7.0

Platforms

For a list of the operating systems and browsers that are supported by Silverlight, see Supported Operating Systems and Browsers.

See Also

Reference

Math Class

System Namespace

E

Pow

Log