How do you check if an integer is a power to another integer in python?

def is_Power[x, y]:
   while [x%y == 0]:
       x = x / y
   return x == 1
print[is_Power[16, 2]]
print[is_Power[12, 2]]
print[is_Power[81, 3]]

True                                                                                                          
False                                                                                                         
True

Given two positive numbers x and y, check if y is a power of x or not.
Examples : 
 

Input:  x = 10, y = 1
Output: True
x^0 = 1

Input:  x = 10, y = 1000
Output: True
x^3 = 1

Input:  x = 10, y = 1001
Output: False

A simple solution is to repeatedly compute powers of x. If a power becomes equal to y, then y is a power, else not. 
 

C++

#include

using namespace std;

bool isPower[int x, long int y]

{

    if [x == 1]

        return [y == 1];

    long int pow = 1;

    while [pow < y]

        pow *= x;

    return [pow == y];

}

int main[]

{

    cout

Javascript

    function isPower[x, y]

    {

        if [x == 1]

            return [y == 1];

        let pow = 1;

        while [pow < y]

            pow = pow * x;

        return [pow == y];

    }

        document.write[[isPower[10, 1] ? 1 : 0] + "
"];

           document.write[[isPower[1, 20] ? 1 : 0] + "
"];

        document.write[[isPower[2, 128] ? 1 : 0] + "
"];

        document.write[[isPower[2, 30] ? 1 : 0] + "
"];

Output: 

1
0
1
0

Time complexity of above solution is O[Logxy]
Optimization: 
We can optimize above solution to work in O[Log Log y]. The idea is to do squaring of power instead of multiplying it with x, i.e., compare y with x^2, x^4, x^8, …etc. If x becomes equal to y, return true. If x becomes more than y, then we do binary search for power of x between previous power and current power, i.e., between x^i and x^[i/2].
Following are detailed step. 

1] Initialize pow = x, i = 1
2] while [pow < y]
   {
      pow = pow*pow 
      i *= 2
   }    
3] If pow == y
     return true;
4] Else construct an array of powers
   from x^i to x^[i/2]
5] Binary Search for y in array constructed
   in step 4. If not found, return false. 
   Else return true.

Alternate Solution : 
The idea is to take log of y in base x. If it turns out to be an integer, we return true. Else false. 
 

C++

#include

#include

using namespace std;

bool isPower[int x, int y]

{

    int res1 = log[y] / log[x];

    double res2 = log[y] / log[x];

    return [res1 == res2];

}

int main[]

{

    cout

Javascript

function isPower[x, y]

{

    var res1 = parseInt[Math.log[y]] /

               parseInt[Math.log[x]];

    var res2 = Math.log[y] /

                  Math.log[x];

    return [res1 == res2];

}

if[isPower[27, 729]]

    document.write["1"];

else

    document.write["0"];

Output : 
 

1

Thanks to Gyayak Jain for suggesting this solution.
This article is contributed by Manish Gupta. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
 

How do you check if a number is a power of another Python?

How do you check if an integer is a power of 2 in Python?

How do you evaluate a power in Python?