Comparing X^Y and Y^X for very large values of X and Y

Given two integer X and Y, the task is compare X^Y and Y^X for large values of X and Y.
Examples:

Input: X = 2, Y = 3 
Output: 2^3 < 3^2 
2³ < 3²
Input: X = 4, Y = 5 
Output: 4^5 > 5^4 

Naive approach: A basic approach is to find the values X^Y and Y^X and compare them which can overflow as the values of X and Y can be large
Better approach: Taking log of both the equations, log(X^Y) = Y * log(X) and log(Y^X) = X * log(Y). Now, these values can be compared easily without overflows.
Below is the implementation of the above approach: 

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to compare x^y and y^x
void compareVal(int x, int y)
{

    // Storing values OF x^y AND y^x
    long double a = y * log(x);
    long double b = x * log(y);

    // Comparing values
    if (a > b)
        cout << x << "^" << y << " > "
             << y << "^" << x;

    else if (a < b)
        cout << x << "^" << y << " < "
             << y << "^" << x;

    else if (a == b)
        cout << x << "^" << y << " = "
             << y << "^" << x;
}

// Driver code
int main()
{
    long double x = 4, y = 5;

    compareVal(x, y);

    return 0;
}

Java

// Java implementation of the approach
import java.util.*;

class GFG
{

// Function to compare x^y and y^x
static void compareVal(int x, int y)
{

    // Storing values OF x^y AND y^x
    double a = y * Math.log(x);
    double b = x * Math.log(y);

    // Comparing values
    if (a > b)
        System.out.print(x + "^" + y + " > " +
                         y + "^" + x);

    else if (a < b)
        System.out.print(x + "^" + y + " < " +
                         y + "^" + x);

    else if (a == b)
        System.out.print(x + "^" + y + " = " +
                         y + "^" + x );
}

// Driver code
public static void main(String[] args)
{
    int x = 4, y = 5;

    compareVal(x, y);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 implementation of the approach
from math import log

# Function to compare x^y and y^x
def compareVal(x, y) :

    # Storing values OF x^y AND y^x
    a = y * log(x);
    b = x * log(y);

    # Comparing values
    if (a > b) :
        print(x, "^", y, ">", y, "^", x);

    elif (a < b) :
        print(x, "^", y, "<", y ,"^", x);

    elif (a == b) :
        print(x, "^", y, "=", y, "^", x);

# Driver code
if __name__ == "__main__" :

    x = 4; y = 5;

    compareVal(x, y);

# This code is contributed by AnkitRai01

C#

// C# implementation of the approach
using System;
class GFG
{

// Function to compare x^y and y^x
static void compareVal(double x, double y)
{

    // Storing values OF x^y AND y^x
    double a = y * Math.Log(x);
    double b = x * Math.Log(y);

    // Comparing values
    if (a > b)
        Console.Write (x + "^" + y + " > " +
                       y + "^" + x);

    else if (a < b)
            Console.Write (x + "^" + y + " < "+
                           y + "^" + x);

    else if (a == b)
        Console.Write (x + "^" + y + " = " +
                       y + "^" + x );
}

// Driver code
static public void Main ()
{
    double x = 4, y = 5;

    compareVal(x, y);
}
}

// This Code is contributed by ajit.

Javascript

<script>
// Javascript implementation of the approach

// Function to compare x^y and y^x
function compareVal(x, y)
{

    // Storing values OF x^y AND y^x
    let a = y * Math.log(x);
    let b = x * Math.log(y);

    // Comparing values
    if (a > b)
        document.write(x + "^" + y + " > "
             + y + "^" + x);

    else if (a < b)
        document.write(x + "^" + y + " < "
             + y + "^" + x);

    else if (a == b)
        document.write(x + "^" + y + " = "
             + y + "^" + x);
}

// Driver code
    let x = 4, y = 5;

    compareVal(x, y);

</script>

Output:

4^5 > 5^4

Time Complexity: O(1)

Auxiliary Space: O(1)