Exponentiation in Modular Arithmetic

Question

I feel like this is a fairly straightforward question, but I've been having a great deal of difficult computing one modular arithmetic expression. It's this:

$9 ≡ 3^a \pmod{17}$

How does one go about approaching a problem like this? I'll feel like the solution is much simpler than I'm making it.

Any help is greatly appreciated! Thanks so much.

Answer 1

Keep multiplying 3 by itself and then dividing by 17 and taking the remainder until you get to 9!

Answer 2

You could use some tool like Fermat little theorem: $3^{16} = 1\pmod {17} \to a = 2, 18, 34, \cdots, 2+16k$,..