Is there a quick way to solve $3^8 \equiv x \mod 17$? 
Is there a quick way to solve $3^8 \equiv x \mod 17$?

Like the above says really, is there a quick way to solve for $x$? Right now, what I started doing was $3^8 = 6561$, and then I was going to keep subtracting $17$ until I got my answer.

Here is a simple way of calculating it, which unfortunately only works for these numbers.
Note that $2^4=16=-1 \pmod {17}$. 
Then
$$3^8=-2^43^8=-2^49^4=-18^4=-1^4=-1 \pmod{17}$$
