Theory of complexity: if problem A is logspace reducible to 2-SAT, is it A in NL?

I'm trying to prove that some problem, A, is in NL. I have found a reduction in the logistical space from A to 2-SAT. Am I right in thinking that this is not enough to prove that A is in NL?

If so, how can you formally prove that a language is in NL? Is it the only way we can do it by providing some non-deterministic decidable TM for A that only uses the log space?