Can I make a polynomial reduction from Bounded ATM which k is written in Unary to Bounded ATM which k is written in binary in which:

f: <M,w,k> —-> <M,w,logk>?

Meaning, M accepts w in k steps if and only if M accepts w in 2^logk step?

the only thing that bothers me is whether taking log out of k can be done in polynomial time (which I think so, but better safe than sorry)…

Thanks!