Fermats Little Theorem, primitive root
Hint: modular inverses are unique, therefore the following holds:

$$2^x \equiv 3 \pmod{p} ~ ~ \iff ~ ~ 2^{-x} \equiv 3^{-1} \pmod{p}$$

Now what is the inverse of $3$ modulo this particular $p$? Can you express it as a power of two modulo $p$? Solve for $x$. If you end up with a negative $x$, use Fermat's little theorem to derive a positive exponent.