# 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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