# Program to compare m^n and n^m

Given two positive integers m and n, the task is to write a program that checks whether m^n is greater than, less than or equal to n^m.

Examples :

Input: m = 3, n = 10
Output: m^n > n^m
Explanation : 3^10=59049 which is greater than 10^3=1000

Input: m = 987654321, n = 123456987
Output: m^n < n^m

A naive approach is to compute m^n and n^m, which causes overflow when m and n are very large.

An efficient approach is to solve this problem using log.

Given LHS = m^n and RHS = n^m.
After taking log on both sides, LHS = n*log(m) and RHS = m*log(n)
Then compare the LHS and RHS.

## C++

 `// CPP program to compare which is greater  ` `// m^n or n^m   ` `#include ` `using` `namespace` `std; ` ` `  `// function to compare m^n and n^m  ` `void` `check(unsigned ``long` `long` `m, unsigned ``long` `long` `int` `n) ` `    ``{ ` `        ``// m^n  ` `        ``double` `RHS = m * (``double``)``log``(n); ` `         `  `        ``// n^m  ` `        ``double` `LHS = n * (``double``)``log``(m);  ` `         `  `        ``if` `( LHS > RHS ) ` `            ``cout << ``"m^n > n^m"``; ` `             `  `        ``else` `if` `( LHS < RHS ) ` `            ``cout << ``"m^n < n^m"``; ` `             `  `        ``else` `            ``cout << ``"m^n = n^m"``; ` `    ``} ` ` `  `// Drivers Code  ` `int` `main() { ` `     `  `    ``unsigned ``long` `long` `m = 987654321, n = 123456987; ` `     `  `    ``// function call to compare m^n and n^m ` `    ``check(m, n); ` `     `  `    ``return` `0; ` `} `

## Java

 `// Java program to compare which  ` `// is greater m^n or n^m  ` `import` `java .io.*; ` ` `  `class` `GFG ` `{ ` `// function to compare ` `// m^n and n^m  ` `static` `void` `check(``long` `m, ``long` `n) ` `{ ` `    ``// m^n  ` `    ``double` `RHS = m * (``double``)Math.log(n); ` `     `  `    ``// n^m  ` `    ``double` `LHS = n * (``double``)Math.log(m);  ` `     `  `    ``if` `(LHS > RHS) ` `        ``System.out.print(``"m^n > n^m"``); ` `         `  `    ``else` `if` `(LHS < RHS) ` `    ``System.out.print(``"m^n < n^m"``); ` `         `  `    ``else` `        ``System.out.print(``"m^n = n^m"``); ` `} ` ` `  `// Driver Code  ` `static` `public` `void` `main (String[] args) ` `{ ` `    ``long` `m = ``987654321``, n = ``123456987``; ` ` `  `    ``// function call to  ` `    ``// compare m^n and n^m ` `    ``check(m, n); ` `} ` `} ` ` `  `// This code is contributed by anuj_67. `

## Python3

 `# Python3 program to compare  ` `# which is greater m^n or n^m  ` `import` `math ` ` `  `# function to compare ` `# m^n and n^m  ` `def` `check( m, n): ` `     `  `    ``# m^n  ` `    ``RHS ``=` `m ``*` `math.log(n); ` `     `  `    ``# n^m  ` `    ``LHS ``=` `n ``*` `math.log(m);  ` `     `  `    ``if` `(LHS > RHS): ` `        ``print``(``"m^n > n^m"``); ` `         `  `    ``elif` `(LHS < RHS): ` `        ``print``(``"m^n < n^m"``); ` `         `  `    ``else``: ` `        ``print``(``"m^n = n^m"``); ` ` `  `# Driver Code  ` `m ``=` `987654321``;  ` `n ``=` `123456987``; ` ` `  `# function call to  ` `# compare m^n and n^m ` `check(m, n); ` ` `  `# This code is contributed by mits `

## C#

 `// C# program to compare which   ` `// is greater m^n or n^m  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `// function to compare ` `// m^n and n^m  ` `static` `void` `check(``ulong` `m, ``ulong` `n) ` `{ ` `    ``// m^n  ` `    ``double` `RHS = m * (``double``)Math.Log(n); ` `     `  `    ``// n^m  ` `    ``double` `LHS = n * (``double``)Math.Log(m);  ` `     `  `    ``if` `(LHS > RHS) ` `        ``Console.Write(``"m^n > n^m"``); ` `         `  `    ``else` `if` `(LHS < RHS) ` `    ``Console.Write(``"m^n < n^m"``); ` `         `  `    ``else` `        ``Console.Write(``"m^n = n^m"``); ` `} ` ` `  `// Driver Code  ` `static` `public` `void` `Main () ` `{ ` `    ``ulong` `m = 987654321, n = 123456987; ` ` `  `    ``// function call to  ` `    ``// compare m^n and n^m ` `    ``check(m, n); ` ` `  `} ` `} ` ` `  `// This code is contributed by anuj_67. `

## PHP

 ` ``\$RHS` `) ` `        ``echo` `"m^n > n^m"``; ` `         `  `    ``else` `if` `( ``\$LHS` `< ``\$RHS` `) ` `    ``echo` `"m^n < n^m"``; ` `         `  `    ``else` `        ``echo` `"m^n = n^m"``; ` `} ` ` `  `// Driver Code  ` `\$m` `= 987654321;  ` `\$n` `= 123456987; ` ` `  `// function call to  ` `// compare m^n and n^m ` `check(``\$m``, ``\$n``); ` ` `  `// This code is contributed by anuj_67. ` `?> `

Output :

`m^n < n^m`

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