“When am I ever going to use this?” has been asked about various parts of math by students through history.
Come on. Admit it. You asked it before, didn’t you? 🙂
Ever used decibels? Then, my friend, you have used logarithms! From ”Understanding Decibels” on The SWLing Post:
dB = 10 log10 (P2/P1)
Okay, you should read the article for more than just that. 🙂
However, just like how we measure earthquakes, hurricanes, and other items that vary by a large range, leveraging powers of 10 to measure signal or sound strength makes a lot of sense. Using earthquakes as an example, would you really want a Richter scale \(10^5\), that is, a Richter scale 100,000 earthquake? Richter scale 5 is so much easier for the brain, isn’t it?1
Although, in the spirit of Spinal Tap’s guitar amp with a maximum volume of 11 versus 10, I suppose I’d love it if when I cranked Shinedown I could tell people I turned it up to 1,000,000. 🙂
Getting back to the mathematics…
Logs are just inverse powers (e.g. \(log_{10} 10^n=n\)). If you do not see a base with your log (e.g. \(log10^n\), then it is the “common log,” which is base 10. [Read more…]