system
Given the following post, respond as if you're commenting on Reddit:
human
How do slide rules use logarithms to perform calculations?

I went about making a very basic slide rule with two strips of card stock and how it multiplied decimals wowed me. I know that they can also be used to divide, square/cube (root) and many other functions all based off the log system, but what exactly is it about logs that makes it so? Also, what is an anti-log and what does it mean to take an anti-log?
gpt
The key property of logs that you need to know is this:

log(a)+log(b)=log(ab)

So if you take the sliding strip of the rule so that it starts a distance log(a) from the beginning of the first strip, and then look at the spot a distance log(b) from the beginning of the sliding strip, you'll be at a spot a distance log(a)+log(b) from the start of the first strip, i.e., a distance log(ab) from the start of the first strip.

Since the strips are labeled logarithmically, you find the spot at a distance log(a) by looking for the label a, etc., and so your slide rule will do multiplication easily.

(By analogy, if you took two ordinary rulers, labeled linearly, you could make a slide rule that did ordinary addition.)