Logs: the chapter that will never end.
As I said at the end of blog post 2, I tried a new way of teaching log equations, using the question, “Hey, what power of ___ gives you ____?”
I decided to jump in with both feet and use the same question for logs on both sides. Normally, I would just cancel them:
But then we’d end up thinking that works for this problem, too:
So I went back to the question:
(Pssst…drawing the box around the right side does help! Also lead in with a reminder of the “easy” ones from the first day of logs. And spend a bit of time talking about why they’re inverses and what inverses do.) Yes, it does seem like we’re taking the long way around but wait until you get to here:
On the quiz, I’d say less than 5% tried to cancel all the logs at once. Some students asked me that since we were doing the same thing to both sides, we know the arguments had to be equal so could they do it that way. I told them that was very neat that they noticed that but warned them against just randomly crossing out logs.
I also did the same with exponentials.
Then everyone that doesn’t have math print on their TI got sad (psst..log with a modifiable base is towards the end of the Math menu), but with a few parentheses we were good to go using the change of base formula.
I must admit I’m not 100% sold on the new exponential way. I’m still having to reinforce that the log helps us answer an exponent question. I still have a few people just make log x = 60 into log 60 =x because aren’t we just randomly moving numbers around anyway? But don’t I have that every year? And, as Conic Card Cindy famously said, they weren’t learning it the old way I taught it, so what’s the worst that could happen?
And just because I like you, here are some more files for you.
Natural Logs! .doc file Yeah, I kind of glossed over the discovery of e. Don’t tell the math police. Although they’re probably on their way after that cross-multiplication I did in #9 above. But the common log lesson is not the time to take away the one thing they remember how to do from middle school. ANYWAY….
Bonus review powerpoint of log laws and common logs! Great for whiteboard practice! Each problem is worked out step by step.