calculating a group element in a discrete log problem An encryption scheme is based on the DLP: $c = a^x mod ~b$, where $x$ is hard to find. How hard is it to find $a$, given all the other values, $c$, $x$ and $b$?

Would this make the problem easy to solve?

$c^{1/x} = (a^x)^{1/x} mod ~b$

An example would be great to better understand.
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.