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# Larger of a^b or b^a (a raised to power b or b raised to power a)

Given two numbers , find which is greater .
If , print a^b is greater
If , print b^a is greater
If , print Both are equal
Examples:

```Input : 3 5
Output : a^b is greater
3^5 = 243, 5^3 = 125. Since, 243>125, therefore a^b > b^a.

Input : 2 4
Output : Both are equal
2^4 = 16, 4^2 = 16. Since, 16=16, therefore a^b = b^a.```

Brute Force solution would be to just compute and compare them. But since can be large enough that can not be stored even in long long int, so this solution is not feasible. Also computing to the power n would require at least time using the fast exponentiation technique.
Efficient approach would be to use logarithm. We have to compare . If we take log, the problem reduces to comparing Hence,
If , print a^b is greater
If , print b^a is greater
If , print Both are equal
Below is the implementation of the efficient approach discussed above.

## C++

 `// C++ code for finding greater``// between the a^b and b^a``#include ``using` `namespace` `std;` `// Function to find the greater value``void` `findGreater(``int` `a, ``int` `b)``{``    ``long` `double` `x = (``long` `double``)a * (``long` `double``)(``log``((``long` `double``)(b)));``    ``long` `double` `y = (``long` `double``)b * (``long` `double``)(``log``((``long` `double``)(a)));``    ``if` `(y > x) {``        ``cout << ``"a^b is greater"` `<< endl;``    ``}``    ``else` `if` `(y < x) {``        ``cout << ``"b^a is greater"` `<< endl;``    ``}``    ``else` `{``        ``cout << ``"Both are equal"` `<< endl;``    ``}``}` `// Driver code``int` `main()``{``    ``int` `a = 3, b = 5, c = 2, d = 4;``    ``findGreater(a, b);``    ``findGreater(c, d);``    ``return` `0;``}`

## Java

 `// Java code for finding greater``// between the a^b and b^a` `public` `class` `GFG{` `    ``// Function to find the greater value``    ``static` `void` `findGreater(``int` `a, ``int` `b)``    ``{``        ``double` `x = (``double``)a * (``double``)(Math.log((``double``)(b)));``        ``double` `y = (``double``)b * (``double``)(Math.log((``double``)(a)));``        ``if` `(y > x) {``            ``System.out.println(``"a^b is greater"``) ;``        ``}``        ``else` `if` `(y < x) {``            ``System.out.println(``"b^a is greater"``) ;``        ``}``        ``else` `{``            ``System.out.println(``"Both are equal"``) ;``        ``}``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main(String []args)``    ``{``        ``int` `a = ``3``, b = ``5``, c = ``2``, d = ``4``;``        ``findGreater(a, b);``        ``findGreater(c, d);``    ``}``    ``// This code is contributed by Ryuga``}`

## Python 3

 `# Python 3 code for finding greater``# between the a^b and b^a``import` `math` `# Function to find the greater value``def` `findGreater(a, b):` `    ``x ``=` `a ``*` `(math.log(b));``    ``y ``=` `b ``*` `(math.log(a));``    ``if` `(y > x):``        ``print` `(``"a^b is greater"``);``    ``elif` `(y < x):``        ``print``(``"b^a is greater"``);``    ``else` `:``        ``print``(``"Both are equal"``);` `# Driver code``a ``=` `3``;``b ``=` `5``;``c ``=` `2``;``d ``=` `4``;``findGreater(a, b);``findGreater(c, d);` `# This code is contributed``# by Shivi_Aggarwal`

## C#

 `// C# code for finding greater``// between the a^b and b^a`` ` `using` `System;``public` `class` `GFG{`` ` `    ``// Function to find the greater value``    ``static` `void` `findGreater(``int` `a, ``int` `b)``    ``{``        ``double` `x = (``double``)a * (``double``)(Math.Log((``double``)(b)));``        ``double` `y = (``double``)b * (``double``)(Math.Log((``double``)(a)));``        ``if` `(y > x) {``            ``Console.Write(``"a^b is greater\n"``) ;``        ``}``        ``else` `if` `(y < x) {``            ``Console.Write(``"b^a is greater"``+``"\n"``) ;``        ``}``        ``else` `{``            ``Console.Write(``"Both are equal"``) ;``        ``}``    ``}``     ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `a = 3, b = 5, c = 2, d = 4;``        ``findGreater(a, b);``        ``findGreater(c, d);``    ``}``    ` `}`

## PHP

 ` ``\$x``)``    ``{``        ``echo` `"a^b is greater"``, ``"\n"``;``    ``}``    ``else` `if` `(``\$y` `< ``\$x``)``    ``{``        ``echo` `"b^a is greater"``, ``"\n"` `;``    ``}``    ``else``    ``{``        ``echo` `"Both are equal"``, ``"\n"` `;``    ``}``}` `// Driver code``\$a` `= 3;``\$b` `= 5;``\$c` `= 2;``\$d` `= 4;``findGreater(``\$a``, ``\$b``);``findGreater(``\$c``, ``\$d``);` `// This code is contributed by ajit``?>`

## Javascript

 ``

Output:

```a^b is greater
Both are equal```

Time Complexity: O(logn), since it is using inbuilt log function

Auxiliary Space: O(1), since no extra space has been taken.

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