# Can we decide if a number is a power of any given \$K\$ in polynomial-time?

It is simple to decide powers of 2 in $$O(n)$$ time because it’s just "0-bit Unary" after bit-1. (eg. $$1000$$ is a power of 2 in binary).

I haven’t found many other trivial powers of $$K$$ that can be decided in polynomial-time with the binary-length of the input.

## Question

Can we decide if a number is a power of any given $$K$$ in polynomial-time and in a practical amount of time?

Something not naive such as keep dividing $$N$$ by $$K$$ until you reach the smallest value $$2$$ for deciding a power of 2.