calculating a group element in a discrete log problem
If you know the factorization of $b$, it's easy.  One way would be to compute $x^{-1}$, the multiplicative inverse modulo $\phi(b)$, and then compute $c^{x^{-1}} \bmod b$

If you don't know the factorization of $b$, it's hard; in fact, it's essentially the RSA problem.