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.

When dealing with powers, squaring is a good trick to reduce computations (your computer does this too!) What this means is:
$ \begin{array}{l l l l l}
3 &             &\equiv 3 &\pmod{17}\\
3^2 &\equiv 3^2 & \equiv 9 &\pmod{17}\\
3^4 & \equiv 9^2 & \equiv 81 \equiv 13 & \pmod{17}\\
3^8 & \equiv 13^2 & \equiv 169 \equiv 16 & \pmod{17}\\
\end{array} $

Slightly irrelevant note: By Euler's theorem, we know that $3^{16} \equiv 1 \pmod{17}$. Thus this implies that $3^{8} \equiv \pm 1 \pmod{17}$. If you know more about quadratic reciprocity, read Thomas Andrew's comment below.
