Logs
Introduction
Like all things I have learned or not learned, I need a pages so I can say, yes I remember this.
Going in Gaussian Naive Bayes I was redirected to logs. This showed how log number lines show the size of the differences. If for instance we take 1 and 8, 8 is 8 times the distance from 1 but if we do this with 1/8th and 1 which is also 8 times the distance the number line does not show this. But a log number line does
Fold Change is defined as Ratio that describes a change in a measured value
Second Time Around
I want to restate this so I don’t forget it. The diagram below shows that I *do* understand logarithms — I just lose the phrasing sometimes.
- The logarithm of 8 in base 2 is 3**
because **2³ = 8**. A logarithm tells you **how many times you multiply the base to reach the value**.
The diagram shows that:
- 8 is *8× bigger* than 1 - 1 is *8× bigger* than 1/8
So on a logarithmic scale, those distances are the same.
- Logarithms measure multiplicative distance.**
---
- Using logs to multiply numbers (the old log‑table method)
To compute:
``` 37 × 59 ```
Convert each number into its base‑10 logarithm:
``` log10(37) = 1.5682 log10(59) = 1.7709 ```
Add the logs:
```
1.5682
+ 1.7709
3.3391
```
Now convert back:
``` 10^3.3391 ≈ 2181 ```
The true product is 2183 — the small difference is rounding error from the log table.
This works because:
> **log(a × b) = log(a) + log(b)** > (multiplication becomes addition)
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If you want, I can also help you add a small section explaining *why* log scales appear everywhere in computing (binary length, entropy, GF256, etc.).