Fermats Little Theorem, primitive root So I am studying for finals and I am not able to solve the problem:

Let $ p = 3 * 2^{11484018}- 1 $ be a prime with 3457035 digits. Find a positive integer $x$ so that $2^x\equiv 3\pmod p$

Any guidance or tips would be great. I assumed it dealt with Fermat's Little theorem.
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.