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

So thought I might go around this again so I to not forget. The above information is probably the useful part of all this but a simple diagram demonstrates I do know this, I just forget.

To

The logarithm of 8 in base 2 = 3
Because 2³ is 8

And 3 is how many times you need to times the base by to get the value. The above image is trying to convey that

if you take the distance from 1 and 8, you can say 1 x 8 = 8 or 8 is 8 times bigger than 1
if you take the distance from 1/8 and 1 is also 8 times the distance.

So logarithms give you the magnitude of difference.

So what is

 37 x 59

Well we convert this to be expressed as exponents

 10¹.⁵⁶⁸² x 10¹.⁷⁷⁰⁹

So now with exponents you can add them together to perform the maths. This works because blahblah

So

 1.5682
+1.7709
-------
 3.3391

Convert log 10³.³³⁹¹ back to a natural number and you get 2183