Even Chloe knows to go to infinitemathideas.com for Math help!
Welcome Chloe fans! I want to throw Chloe a bone (literally) for providing the first external link to our Math blog! Although she has thousands of subscratchers and this blog only has 12 (counting my mother…), we feel it’s a fair exchange. Here is the email exchange that started Chloe’s love of math! Chloe fans who have children in school may want to read this article.
So on the topics of old tricks for new dogs, I want to talk about a better (in my opinion) way to teach (and learn) logs (think really large sticks Chloe…). Specifically converting to and from exponential forms.
Bacon and Eggs go Vegan.
Using inverse functions instead of “Bacon N Eggs”
I have a big secret. When I first taught Algebra 2, I really didn’t fully understand (or enjoy) logarithms. I could teach the rules, etc. but I just didn’t get it – that is until I threw away the bacon (ironically about the same time I became a vegetarian). I’m talking about Bacon N Eggs (Base – number – exponent) – a trick that we teach students to use when converting between log form and exponential form. Don’t get me wrong, I still use and teach using Mnemonics such as FOIL and SOH-CAH-TOA but only after (hopefully) an exhaustive explanation of why they work. The problem is that what’s really going on is the same technique we use at all levels of Algebra – and Bacon and Eggs doesn’t help reinforce this important skill. It’s simply applying the inverse function to both sides of an equation. Here is how I show students now how to solve log equations.
Solving Log equations by doing the inverse function to both sides
Inverse functions – my favorite old trick.
I’m a big fan of Common core. The testing may be controversial but the curriculum framework is something we’ve been doing here for years. This includes more real life application problems and making students explain and justify answers (to name just a few). But I’ve been told (though I haven’t checked it out myself) that they have downplayed inverse functions. I couldn’t disagree more. Even when we teach Algebra 1 we literally explain that we are actually doing the inverse function to both sides. With logs, we show that exponential functions graphically are inverses of logarithm functions and then we apply this to solve log equations. Connecting this technique to solving trig and basic Algebra 1 equations brings it all together for students and eliminates the “magic” (or voodoo) that impedes understanding. When students know why something works (instead of just how), they retain the skill and (I believe) learn to enjoy math.
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