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[silverspawn]

log!

[liopoil]

What the hell is a log with base pi? Is that something that would ever be used?

[Tables]

What the hell is a log with base pi? Is that something that would ever be used?

About the only application I can think of is for finding the dimension of a hypersphere or something like that...  which isn't really something you need to do.

[qmech]

I asked a group of mathematicians what they thought the base of ld was today.  The first guess was 10.  The second guess was pi.

[WalrusMcFishSr]

What the hell is a log with base pi? Is that something that would ever be used?

About the only application I can think of is for finding the dimension of a hypersphere or something like that...  which isn't really something you need to do.

What's the deal with the fact that the exponent of pi goes up only every two dimensions? That always sort of bothered me, is there an intuitive explanation for that?

[HiveMindEmulator]

Totally depends on context. In theoretical science it's base e. In computer science it's base 2. In practical science, it's base 10. And in this context, I thought it was a record of what happened in a game of Dominion...

[silverspawn]

Totally depends on context. In theoretical science it's base e. In computer science it's base 2. In practical science, it's base 10. And in this context, I thought it was a record of what happened in a game of Dominion...

option added

[GeoLib]

Totally depends on context. In theoretical science it's base e. In computer science it's base 2. In practical science, it's base 10. And in this context, I thought it was a record of what happened in a game of Dominion...

option added

Wait that's basically what I said in my comment. How do I change my vote?

[rrenaud]

As a computer scientist, all I've gotta say is that

O(log_a(x)) = O(log_b(x)) for all a > 1, b > 1.

So it doesn't matter, it's just a constant factor difference ;P.

[silverspawn]

Totally depends on context. In theoretical science it's base e. In computer science it's base 2. In practical science, it's base 10. And in this context, I thought it was a record of what happened in a game of Dominion...

option added

Wait that's basically what I said in my comment. How do I change my vote?

dunno, but it should be possible, there's a checkbox "allow users to change votes" when creating a poll and i enabled it

[sudgy]

All of you who say "log is base e", give up.  2.71828... voted log is base 10

[2.71828.....]

All of you who say "log is base e", give up.  2.71828... voted log is base 10

Well, that is primarily because of the indoctrination of the American high school system that taught log(x) implied log₁₀(x) and that for base e you always use ln.  However, I do think that this does fall into some of the same discussion surrounding 7 – 4 + 3 x 0 + 1 = ?.  Namely that when such a term is used the author will not be purposely ambiguous.  Either you will know from context or he will explicitly state what base he means to use.

[Davio]

As a computer scientist, all I've gotta say is that

O(log_a(x)) = O(log_b(x)) for all a > 1, b > 1.

So it doesn't matter, it's just a constant factor difference ;P.

As a computer programmer, I voted for 10.

make sure you read that correctly (:

[SirPeebles]

All of you who say "log is base e", give up.  2.71828... voted log is base 10

Well, that is primarily because of the indoctrination of the American high school system that taught log(x) implied log₁₀(x) and that for base e you always use ln.  However, I do think that this does fall into some of the same discussion surrounding 7 – 4 + 3 x 0 + 1 = ?.  Namely that when such a term is used the author will not be purposely ambiguous.  Either you will know from context or he will explicitly state what base he means to use.

It is often implemented in software without much warning (unless you RTFM).  If I forget to mention this to my students, there will always be a few who use log to mean base 10 and then complain that their online homework was marked wrong.

[DG]

I guess I'm the only person who thought of http://www.boardgamegeek.com/boardgame/1816/mississippi.

[GendoIkari]

[Kuildeous]

As a computer programmer, I voted for 10.

make sure you read that correctly (:

Davio wins. All other arguments are futile.

[Witherweaver]

Or you could, you know, think about how you define the function x -> log(x).  Using the non-natural base is silly.

[pacovf]

Or you could, you know, think about how you define the function x -> log(x).  Using the non-natural base is silly.

A function that transforms products into sums?

(i.e, f such as f(a*b) = f(a) + f(b) )

[DStu]

Or you could, you know, think about how you define the function x -> log(x).  Using the non-natural base is silly.

log(x) := (x -> 2^x)^(-1) ?

[Witherweaver]

Or you could, you know, think about how you define the function x -> log(x).  Using the non-natural base is silly.

A function that transforms products into sums?

(i.e, f such as f(a*b) = f(a) + f(b) )

How do you actually show the only such function is a logarithm?  (That is true, right)?  I might guess that any way you do it, the natural base will kind of fall out.

[Witherweaver]

Or you could, you know, think about how you define the function x -> log(x).  Using the non-natural base is silly.

log(x) := (x -> 2^x)^(-1) ?

Seems a bit random to me.  Why didn't you use pi?

[Witherweaver]

Or x^2.  Or x^pi.  Or sin(x).  Or anything.  What's special about x->2^x?  There's no structure in that definition. 

[DStu]

Or you could, you know, think about how you define the function x -> log(x).  Using the non-natural base is silly.

log(x) := (x -> 2^x)^(-1) ?

Seems a bit random to me.  Why didn't you use pi?

actually I thought on using 5...

edit: And seriously, maybe because 2^x is the exponent that naturally appears in your field...
edit2: And what I actually want to hint on is: "How you define log" is not really a reason for one variant, as there are thousands of ways to define log, what's probably more important is "why you define log the way you do", but both "how" and "why" probably depends on context.

[DStu]

Or you could, you know, think about how you define the function x -> log(x).  Using the non-natural base is silly.

A function that transforms products into sums?

(i.e, f such as f(a*b) = f(a) + f(b) )

How do you actually show the only such function is a logarithm?

You just defined that as the defining property of the logarithm, how can it not be one?

More importantly is probably the question of existence...