### GIGAMIND

Folder:

113 Math

File:

113.021 Logarithms

# Logarithms

At it's most simple, a logarithm is just something that, given a power of ten, spits out the number of zeros at the end of it.

`log(1) = 0`

`log(10) = 1`

`log(100) = 2`

`log(1,000) = 3`

`log(10,000) = 4`

Most of the time when you see `log()`

it is referring to log base 10.

$$log_{10}()$$

There is a convention in math where often `log()`

is referring to `log_e() = ln()`

(but I need to learn more about this)

$$log_e()$$

`log(a * b) = log(a) + log(b)`

- Intuitive because you're just counting the number of zeros like this:

- $$(log(1,000) + log(100)) = log(1,000 \times 100) = log(100,000) = 5$$

The earthquake scale is `log_32`

. An 8.0 seismic earthquake is 32X larger than a 7.0 earthquake (which is, of course, 32X larger than a 6.0).

Decibels are a logarithmic scale.

##### Source:

- Logarithm Fundamentals https://www.youtube.com/watch?v=cEvgcoyZvB4

##### Tags:

- math