### 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.