# Logarithms in any base-what are they used for?

**URL:** <https://boards.straightdope.com/t/logarithms-in-any-base-what-are-they-used-for/224041>\
**Category:** Factual Questions\
**Created:** [January 11, 2004, 8:40pm UTC](https://boards.straightdope.com/t/logarithms-in-any-base-what-are-they-used-for/224041 "2004-01-11T20:40:55Z")\
**Posts on this page:** 3\
**Page:** 2

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**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\
**Post date:** [January 12, 2004, 7:42am UTC](https://boards.straightdope.com/t/logarithms-in-any-base-what-are-they-used-for/224041/21 "2004-01-12T07:42:34Z")

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> [@](#):
>
> \*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. 🙂

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**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\
**Post date:** [January 12, 2004, 11:57am UTC](https://boards.straightdope.com/t/logarithms-in-any-base-what-are-they-used-for/224041/22 "2004-01-12T11:57:29Z")

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**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_

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**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\
**Post date:** [January 12, 2004, 12:16pm UTC](https://boards.straightdope.com/t/logarithms-in-any-base-what-are-they-used-for/224041/23 "2004-01-12T12:16:19Z")

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> [@](#):
>
> \*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].

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