Logarithms in any base-what are they used for?

[Achernar]

*Originally posted by Derleth *
Oh, and computers don’t use binary, either. They use electrical currents and switches (aka transistors).

You have a good point, but that statement seems a bit extreme. I hope if someone says, “Computer use binary.” you don’t respond with “Yeah? You’re wrong.” and walk away laughing.

[Jabba]

wolf_meister said:

However, Jabba, I have to agree with Sunspace that whenever I see ‘log’ without any base specified, I always think of it as log10 and not natural log

In mathematics, since logs to the base 10 aren’t used, log is used to denote log[sub]e[/sub]. For example,

“log x is, of course, the ‘Naperian’ logarithm of x to the base e. ‘Common’ logarithms have no mathematical interest.”
G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers

“Since e[sup]x[/sup] is strictly increasing and differentiable on R, it has an inverse function L… The customary notation for L(x) is of course log x.”
W. Rudin, Principles of Mathematical Analysis

[Desmostylus]

*Originally posted by Jabba *
**wolf_meister said:

In mathematics, since logs to the base 10 aren’t used, log is used to denote log[sub]e[/sub].**

I think you’re pushin’ it a bit there, Jabba. The log/ln notation is standard in undergrad calculus texts, on the keys of calculators, etc.

Originally posted by friedo
There aren’t really “octal or hexidecimal computing systems,” just binary systems that are convenient to represent in octal or hexidecimal for us stoopid hoomans.

The distinction actually does arise occasionally. Before the IEEE floating point standard became “standard”, IBM machines (other than PCs) used a hex radix for floating point numbers. That is, floating point numbers were stored as nnnnnnn x 16[sup]nnnn[/sup] rather than nnnnnnn x 2[sup]nnnn[/sup].