# Find larger of x^y and y^x

Given two integer numbers X and Y. find the larger of X^Y and Y^X, or determine if they are equal.

Examples:

Input : 2 3
Output : 3^2
We know 3^2 = 9 and 2^3 = 8.

Input : 2 4
Output : Equal

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A simple solution is calculate x^y by looping for y times, but if the values of x and y is too large it will cause overflow.

To solve the overflow problem, we can simplify the equation by taking log.
log(x^y) = y* log(x)
Now, this equation will not cause overflow and we can compare two values directly.

## C++

 // C++ program to print greater of x^y and // y^x #include using namespace std;    void printGreater(double x, double y) {     long double X = y * log(x);     long double Y = x * log(y);     if (abs(X - Y) < 1e-9) {         cout << "Equal";     }     else if (X > Y) {         cout << x << "^" << y;     }     else {         cout << y << "^" << x;     } }    int main() {     double x = 5, y = 8;     printGreater(x, y);     return 0; }

## Java

 // Java program to print  // greater of x^y and y^x import java.io.*;    class GFG { static void printGreater(int x,                          int y) {     double X = y * Math.log(x);     double Y = x * Math.log(y);     if (Math.abs(X - Y) < 1e-9)     {         System.out.println("Equal");     }     else if (X > Y)     {         System.out.println(x + "^" + y);     }     else     {         System.out.println(y + "^" + x);     } }    // Driver Code public static void main (String[] args)  {     int x = 5, y = 8;     printGreater(x, y); } }    // This code is contributed  // by anuj_67.

## Python3

 # Python3 program to print greater  # of x^y and y^x import math    def printGreater(x, y):        X = y * math.log(x);     Y = x * math.log(y);     if (abs(X - Y) < 1e-9):         print("Equal");     elif (X > Y):         print(x, "^", y);     else:         print(y, "^", x);    # Driver Code x = 5; y = 8; printGreater(x, y);    # This code is contributed by mits

## C#

 // C# program to print  // greater of x^y and y^x using System;    class GFG { static void printGreater(int x,                           int y) {     double X = y * Math.Log(x);     double Y = x * Math.Log(y);     if (Math.Abs(X - Y) < 1e-9)     {         Console.WriteLine("Equal");     }     else if (X > Y)     {         Console.WriteLine(x +                            "^" + y);     }     else     {         Console.WriteLine(y +                            "^" + x);     } }    // Driver Code public static void Main ()  {     int x = 5, y = 8;     printGreater(x, y); } }    // This code is contributed  // by anuj_67.

## PHP

 \$Y)      {         echo \$x . "^" . \$y;     }     else      {         echo \$y . "^" . \$x;     } }    // Driver Code \$x = 5; \$y = 8; printGreater(\$x, \$y);    // This code is contributed by mits ?>

Output:

5^8

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