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

We have discussed two different approaches in below post.

Check if a number can be expressed as x^y (x raised to power y).

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 <bits/stdc++.h>` `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

`<?php` `// PHP program to find if a number` `// can be expressed as x raised to` `// power y.` ` ` `function` `isPower(` `$n` `)` `{` ` ` `// Find Log n in different ` ` ` `// bases and check if the ` ` ` `// value is an integer` ` ` `for` `(` `$x` `= 2; ` `$x` `<= sqrt(` `$n` `); ` `$x` `++) ` ` ` `{` ` ` `$f` `= log(` `$n` `) / log(` `$x` `);` ` ` `if` `((` `$f` `- (int)` `$f` `) == 0.0) ` ` ` `return` `true; ` ` ` `}` ` ` `return` `false;` `}` ` ` `// Driver code` `for` `(` `$i` `= 2; ` `$i` `< 100; ` `$i` `++)` ` ` `if` `(isPower((int)` `$i` `))` ` ` `echo` `$i` `.` `" "` `;` ` ` `// This code is contributed by Sam007` `?>` |

**Output:**

4 8 9 16 25 27 32 36 49 64 81

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