Understand Logarithms with the Help of this Simple Triangle

Trevor English

If you remember your math classes, you may not have understood logarithms, as in most cases they aren't taught very well. Why in the world would anyone ever dream up a notation that seems more confusing than just writing the actual expression? While logarithms are useful in their own right, there is a huge teaching gap between the relation of logarithms to exponents and roots. For the most part, kids learn these notations and equations as separate entities, which can become confusing when you start seeing them together. However, one Youtuber has come up with a triangle that perfectly explains logarithms in relation to roots and exponents. Check it out below.


Math isn't bound by notation, and it is a lot more than just numbers on a page, but in terms of logarithms, it seems to be more confusing than it is helpful. Different notations of the equation 23=8 seem like different programming languages in their own right. Why learn the same thing three different ways if you can interconnect them and learn it all at once?

This new triangle method may be too visual for some of you more analytically minded. For many learning math, however, this visual method of relating numbers could prove essential to understanding these mathematical notations. Through visual cues in the placement of numbers on the triangle, you can denote the notion as well as the answer. Check out the image below and study it to see how the notation and position on the triangle are interrelated.

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logarithm triangle[Image Source: 3Blue1Brown]

One of the main reasons I became an engineer was because I had a phenomenal math teacher in high school that made it simple to understand. Unfortunately, many don't have that luxury and are turned away from engineering and technical fields because they "just don't get it." Hopefully this new triangle method will help many understand logarithms and maybe inspire some engineers down the line.

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