Interesting math problem

Hello! My teacher gave me this question for extra credit the other day that I cannot solve Anyways I thought it was kind of cool. If you could help me that'd be great.
Find all positive integer solutions to$$2^a +1=3^b$$

One solution I found is a=b=1 because 2+1=3, but I don't know any other solutions.

Yeah I also found a=3 and b=2. I'm pretty sure there's no more solutions but I don't know how to prove that