Logs are awesome.
Do you think logarithms are made-up functions just so your math teachers will have more random rules for you to memorize? Think again! Here is a list of reasons logarithms are useful for understanding the world.
- Many scales for measurement involving our senses are logarithmic. Fechner's Law states that "Subjective sensastion is proportional to the logarithm of the stimulus intensity".
- Decibels - Think of this: If you are standing next to a jet engine, and somebody turns on a radio, you are not going to notice a difference in the sound level. The sound needs to multiply - for instance by turning on
another jet engine - for you to notice a difference in the sound level. - Richter scale. Historical data for earthquakes can be found here: http://earthquake.usgs.gov/earthquakes/eqinthenews/2012/
- Star luminosity
- Pitch
- Decibels - Think of this: If you are standing next to a jet engine, and somebody turns on a radio, you are not going to notice a difference in the sound level. The sound needs to multiply - for instance by turning on
- Our brains have a natural number sense that is logarithmic - it's just been forgotten after years of our linear number system being drilled into our brains. To hear all about this, listen to this radiolab episode.
- Logs give us a convenient way to deal with measurements that involve very large numbers.
- The comic on the right (by the brilliant Randall Munroe at xkcd) attempts to describe distances in the observable universe. Distances are depicted on a logarithmic scale - each step up is double the distance. Imagine doing this on a linear scale. It would be ridiculous.
- pH (measures the acidity and alkalinity of liquids).
This image and more explanation about why pH uses a log scale here
