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Math.Exp Method

Silverlight

Returns e raised to the specified power.

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

[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.
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
*/