Tag: logarithms
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How notation gets in the way of understanding [mathjax]The other day I tweeted this: Objectively, I realize that \(\sqrt2\), \(\log6\), and \(\frac57\) are all specific numbers and that they’re the simplest way to write those specific numbers. But I struggle with convincing my brain of that. And if I struggle, I don’t at all wonder…
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[mathjax]In this item, I will show how the basic logarithmic rules, including the Change of Base formula, follow from this equivalency: \[\log_b m = n \Leftrightarrow b^n = m\] For the ease of reading, I’ll generally use the natural base (\(e\)) and the natural logarithm (\(\ln\)). However, everything here applies to all valid bases (\(b…
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I’m going to talk about logs here. I have more to say later, but this is a basic intro sketch. First I’m going to talk about the stuff of elementary school. When it comes to mathematics, most people find comfort in elementary school mathematics. So, consider the humble number line: We want to move along…
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[mathjax]I used to hate logarithms. They were hopelessly confusing. Sort of like this: https://www.smbc-comics.com/comic/operations This is the third year now that I’ve been teaching Algebra II. Each year, my understanding of logarithms increases, and my love increases in kind. One reason I disliked logarithms is because of the way in which we tend to compartmentalize…