Check if a number is power of k using base changing method
This program checks whether a number n can be expressed as power of k and if yes, then to what power should k be raised to make it n. Following example will clarify :
Input : n = 16, k = 2 Output : yes : 4 Explanation : Answer is yes because 16 can be expressed as power of 2. Input : n = 27, k = 3 Output : yes : 3 Explanation : Answer is yes as 27 can be expressed as power of 3. Input : n = 20, k = 5 Output : No Explanation : Answer is No as 20 cannot be expressed as power of 5.
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We have discussed two methods in below post
:Check if a number is a power of another number
In this post, a new Base Changing method is discussed.
In Base Changing Method, we simply change the base of number n to k and check if the first digit of Changed number is 1 and remaining all are zero.
Example for this : Let’s take n = 16 and k = 2.
Change 16 to base 2. i.e. (10000)2. Since first digit is 1 and remaining are zero. Hence 16 can be expressed as power of 2. Count the length of (10000)2 and subtract 1 from it, that’ll be the number to which 2 must be raised to make 16. In this case 5 – 1 = 4.
Another example : Let’s take n = 20 and k = 3.
20 in base 3 is (202)3. Since there are two non-zero digit, hence 20 cannot be expressed as power of 3.
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