Given log3(3b + 1) - log3(a-2) = -1 for a > 2. Express b in terms of a.

We can start by recognising one of our properties of log. That is log_a(x) - log_a(y) = log_a(x/y). Performing this on our question we get: log₃((3b+1)/(a-2)) = -1. Now we can remove our log and rewrite our equation as follows: (3b+1)/(a-2) = 3^-1 implying that (3b+1) = (a-2)/3 implying that 3b = (a-2)/3 - 1 or better, inserting the -1 into our fraction and getting (a-5)/3. Finally implying that b = (a-5)/9.