I'm going along, happily teaching logs and 10^x and e^x and ln(x) and making sure to put in cool examples and practice and descriptions. I especially was proud of my continual stressing to them to ask the question of themselves, "what is it asking for?" when faced with the equation y = "log base something of something".
I made sure to stress that log of a particular base can be rewritten in an exponential form and visa versa, and I said that they basically represent the same information. I also made sure to stress that logs of a base and that base to a power are inverse operations of each other. Can you see where I'm going with this one?
Well. Today when a student was reviewing for a test she casually mentioned that in the equation y = log a c you can just replace the right hand side with a^c because it means the same thing. Argh. Big miscommunication. I hopefully cured her of her nonunderstanding, but how many other kiddies are lurking out there thinking the same thing?