Clearly, I've just finished my unit on exponentials and logarithms (based upon the fact that I've continuously posted about activities I've done with my class). To start the unit, I always begin with graphing and the conversion between the two different forms (Snail Method).
Typically, the kids have an easy time with the exponentials (side from a few who can't get over the fact that they aren't graphing lines) but struggle with the logs. With logs, I explain that they must find their asymptotes and then convert the log into exponential form to plug in for y and solve for x.
Eventually, they get the hang of it and then understand more so how the two functions are inverses of one another. If I still taught inverses, I'd engage in more of the conversation of how functions who are inverses swap their x and y values thus why we can utilize this logic (now a precalc topic).
As you can see, there are 6 stations, each with a different function. At each station, the kids must graph the function showing their x/y table with domain/range. After 25 minutes, we talked about two of their difficult stations. This was then turned in as an Exit Ticket.
p.s. my kids decided they'd rather just sit and so they wrote down each function then went to their seats.... I should have posted them around the school.....