No, I didn't misspell algorithms in the title.

Logarithms are percieved to be very difficult, or even mysterious. If you take the time to understand them, however, they're not mysterious or difficult, and they can even make some things easier for you! Let's get right to the basics.

If you're familiar with exponents, such as 10², logarithms are basically just a way of rearranging the exponent problem in a different way. This video will explain that idea in a little more detail:



While that boils down what logarithms are, the only real use they describe in that video is the pH of pool water, and it doesn't delve into that much. Over at BetterExplained.com, they have a great article on Using Logarithms In The Real World that gives you a better grasp of their importance. It's a must read on the topic!

As you can see in the graphic up in the corner, logs are easily calculated on many calculators, and computers. However, Numberphile has an excellent lesson in working with logarithms without aid from electronics:



Besides showing the use of log tables, this video also introduces one of my favorite aspects of logarithms. It takes most arithmetic operations and simplifies them in an interesting way. Multiplication becomes addition, division becomes subtraction, exponents become multiplication, and roots become division. In short, logarithms can almost seem like cheating, as they turn more difficult operations into simpler ones!

Even though you see seemingly endless pages of log tables in the video above, it is possible to work out logs in your head, and with much less memorization than you might think. I be derelict in my duty at Grey Matters if I didn't show you how to do something along these lines!

Nerd Paradise has an excellent lesson on working out base 10 logs in your head, and the comments feature several great additional tips. CuriousMath.com used to have a similarly great lesson, which has been rescued by the Internet Wayback Machine. The comments here are also quite helpful.

A lesson in working on exponential problems through logs has also been rescued. The 3rd example, involving finding 5th roots, is surprisingly simple, once you've mastered the basics.

You don't even need to do any mental calculation to take advantage of the power of logarithms. Go back and read my Benford's Law post. It features a quick lesson from James Grime and a Scam School video that shows you how to take advantage of Benford's Law in a very clever way.

Take some time and learn about logarithms. There's plenty to discover, learn, and enjoy about them!