# Check if a number can be expressed as power | Set 2 (Using Log)

Check if a number can be expressed as x^y (x raised to power y)
Given a positive integer n, find if it can be expressed as x^y where y > 1 and x > 0. x and y both are integers.

Examples :

```Input:  n = 8
Output: true
8 can be expressed as 2^3

Input:  n = 49
Output: true
49 can be expressed as 7^2

Input:  n = 48
Output: false
48 can't be expressed as x^y
```

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

We have discussed two different approaches in below post.

The idea is find Log n in different bases from 2 to square root of n. If Log n for a base becomes integer then result is true, else result is false.

## C++

 `// CPP program to find if a number ` `// can be expressed as x raised to ` `// power y. ` `#include ` `using` `namespace` `std; ` ` `  `bool` `isPower(unsigned ``int` `n) ` `{ ` `    ``// Find Log n in different bases ` `    ``// and check if the value is an ` `    ``// integer ` `    ``for` `(``int` `x=2; x<=``sqrt``(n); x++) { ` `        ``float` `f = ``log``(n) / ``log``(x); ` `        ``if` `((f - (``int``)f) == 0.0)  ` `            ``return` `true``;         ` `    ``} ` `    ``return` `false``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``for` `(``int` `i = 2; i < 100; i++) ` `        ``if` `(isPower(i)) ` `            ``cout << i << ``"  "``; ` `    ``return` `0; ` `} `

## Java

 `// Java program to remove all the ` `// characters other then alphabets ` `class` `GFG { ` `     `  `    ``static` `boolean` `isPower(``int` `n) ` `    ``{ ` `        ``// Find Log n in different ` `        ``// bases and check if the  ` `        ``// value is an integer ` `        ``for` `(``int` `x = ``2``; x <=  ` `               ``(``int``)Math.sqrt(n); x++)  ` `        ``{ ` `            ``float` `f = (``float``)Math.log(n) /  ` `                      ``(``float``) Math.log(x); ` `                       `  `            ``if` `((f - (``int``)f) == ``0.0``)  ` `                ``return` `true``;      ` `        ``} ` `        ``return` `false``; ` `    ``} ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``for` `(``int` `i = ``2``; i < ``100``; i++) ` `            ``if` `(isPower(i)) ` `                ``System.out.print( i + ``" "``); ` `    ``} ` `} ` ` `  `// This code is contributed by Sam007 `

## Python3

 `# Python3 program to find if a number ` `# can be expressed as x raised to ` `# power y. ` `import` `math ` ` `  `def` `isPower(n): ` ` `  `    ``# Find Log n in different  ` `    ``# bases and check if the  ` `    ``# value is an integer ` `    ``for` `x ``in` `range``(``2``,``int``(math.sqrt(n)) ``+` `1``):  ` `     `  `        ``f ``=` `math.log(n) ``/` `math.log(x); ` `        ``if` `((f ``-` `int``(f)) ``=``=` `0.0``):  ` `            ``return` `True``;      ` `     `  `    ``return` `False``; ` ` `  `# Driver code ` `for` `i ``in` `range``(``2``, ``100``): ` `    ``if` `(isPower(i)): ` `        ``print``(i, end ``=` `" "``); ` ` `  `# This code is contributed by mits `

## C#

 `// C# program to remove all the ` `// characters other then alphabets ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `    ``static` `bool` `isPower(``int` `n) ` `    ``{ ` `        ``// Find Log n in different ` `        ``// bases and check if the  ` `        ``// value is an integer ` `        ``for` `(``int` `x = 2;  ` `                 ``x <= (``int``)Math.Sqrt(n); x++)  ` `        ``{ ` `            ``float` `f = (``float``)Math.Log(n) /  ` `                      ``(``float``) Math.Log(x); ` `            ``if` `((f - (``int``)f) == 0.0)  ` `                ``return` `true``;      ` `        ``} ` `        ``return` `false``; ` `    ``} ` `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``for` `(``int` `i = 2; i < 100; i++) ` `            ``if` `(isPower(i)) ` `                ``Console.Write( i + ``" "``); ` `    ``}  ` `} ` ` `  `// This code is contributed by Sam007 `

## PHP

 ` `

Output:

```4  8  9  16  25  27  32  36  49  64  81
```

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