## Introduction #

In the early 1600s, a Scottish necromancer took two Greek words, smashed them together, and published in Latin. Ok, maybe he didn't really raise the dead. But I'd imagine that whatever pain would be involved in doing so pales in comparison to the horrors faced by math students when introduced to this Scotsman's word: logarithm.

Historically, logarithms were a revolutionary tool for making computations easier. Yet in my teaching experience, I've found many a student grow frustrated when needing to understand them. And I don't think I'll get much push-back for suggesting that logarithms are one of the more difficult topics for precalculus mathematics courses. My YouTube audience would seem to agree.  Looks like it's time for a lesson on logarithms!

But what exactly makes learning about them so difficult? Maybe it's the need to move beyond the basic operations of addition, subtraction, multiplication, and division. Possibly it's the usage of functions and other mathematical abstractions. Or perhaps it's the intimidating nature of the word itself.

Rather than discuss a topic with which a large percentage of viewers wouldn't be comfortable, I figured this would be a perfect opportunity to put together a math lesson—so welcome to Topics That T-West Thinks Everyone Should Know About Logarithms!

We'll cover the following:

• Where the word logarithm comes from and what it means.

• The relationship between logarithms and exponents.

• How logarithms turn difficult multiplications into easier additions.

• The intuition driving various logarithm formulas and properties.

• What is natural about the natural logarithm and the number $e\text{.}$

• And why logarithms result in fast algorithms and slow growth.

Oh, and we'll discuss some Scottish necromancy along the way.