# What exactly do e, Log and ln mean in math

**URL:** <https://boards.straightdope.com/t/what-exactly-do-e-log-and-ln-mean-in-math/264157>\
**Category:** Factual Questions\
**Created:** [September 12, 2004, 6:47pm UTC](https://boards.straightdope.com/t/what-exactly-do-e-log-and-ln-mean-in-math/264157 "2004-09-12T18:47:24Z")\
**Posts on this page:** 2\
**Page:** 2

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**Author:** ![Orbifold](https://avatars.discourse-cdn.com/v4/letter/o/779978/32.png) [@Orbifold](https://boards.straightdope.com/u/Orbifold)\
**Post date:** [September 14, 2004, 6:35pm UTC](https://boards.straightdope.com/t/what-exactly-do-e-log-and-ln-mean-in-math/264157/21 "2004-09-14T18:35:29Z")

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> [@Voyager](#):
>
> It turns out that using e (2.7 … it’s irrational) has some interesting properties…

In my calculus classes, I prefer to use log(x) to mean log[sub]e/sub because of one such “interesting property”, namely the derivative. The derivative of log[sub]e/sub is just 1/x, while the derivative of log[sub]10/sub is log[sub]10/sub/x. Rather than try to remember that ugly-looking constant every time, I just use e as the base of my logarithms by default. There’s a similar justification for using radians to measure angles: using radians the derivative of sin(x) is cos(x), but using degrees the derivative of sin(x) is cos(x)\*pi/180. Ugly-looking constants and bad and should be set to 1 whenever it’s reasonable to do so, IMO.

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**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\
**Post date:** [September 14, 2004, 8:45pm UTC](https://boards.straightdope.com/t/what-exactly-do-e-log-and-ln-mean-in-math/264157/22 "2004-09-14T20:45:36Z")

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> [@Orbifold](#):
>
> In my calculus classes, I prefer to use log(x) to mean log[sub]e/sub because of one such “interesting property”, namely the derivative. The derivative of log[sub]e/sub is just 1/x, while the derivative of log[sub]10/sub is log[sub]10/sub/x. Rather than try to remember that ugly-looking constant every time, I just use e as the base of my logarithms by default.

That is exactly the interesting property I was thinking of - but I didn’t want to bring up calculus for someone who was having trouble with logs. And come to think of it, log base 10 doesn’t seem to be used much past pre-calculus, especially now that we don’t have humungo slide rules in the front of high school math classes.

As for me, things started breaking down when we got to imaginary exponents. I think it’s genetic - Feynman’s description of how he got calculus intuitively is profoundly disheartening.

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