INX question.

[scguy]

It might sound like a stupid question but when not dealing with logs is it ok to integrate 1/x into INX? The reason i ask is because the course i am doing right now does not directly state that this applies to all cases ie when not dealing with natural logs involving INX, ie:

 

1/x dx= INX (1)

and INX dx= XINX-X (2)

 

So, is (1) true for all cases?

[matt grime]

Well, if you put an integral sign at the front, of course the integral of 1/x wrtx id log(x), give or take a constant. Note, it is common practice to use log for natural log, rather than ln.

 

Just because a question doesn't mention sometihng doesn't mean the answer won't. I presume you're ok with integrating x to get x^2/2, but the "question" deosn't mention quadratics does it?

[scguy]

I know how to integrate terms etc but i just was not to sure about INX and 1/x with regards to logs etc.

[Johnny5]

Note' date=' it is common practice to use log for natural log, rather than ln.

[/quote']

 

 

Actually, in the states at least, it is common practice to write ln (x), and that is an L not an i.

 

Certainly this has been my experience regarding various texts.

 

Log is used for base ten, and log_a (x) for arbitrary bases.

 

When the latex is working again, I will try and answer this. I have a treatise on the integral calculus on this exact question, and as I recall, the answer was exceedingly clear, and I've never read a better discussion on the natural log before, or since. I'll find it and post the answer here, using latex, if they ever get it working again that is.

 

Regards

[matt grime]

What kind of texts Johnny? Speaking as a professional mathematician who's worked in both the US and the UK I'd say that log is the one I'd expect to read in any paper or decent book. Of course if you're basing this on reading some engineering text...

[Johnny5]

What kind of texts Johnny? Speaking as a professional mathematician who's worked in both the US and the UK I'd say that log is the one I'd expect to read in any paper or decent book. Of course if you're basing this on reading some engineering text...

 

Well i have hundreds of books, graduate level mostly.

 

In the overwhelming majority, ln is used exclusively for natural log.

 

And in complex variables, Ln (x) is used.

 

I'd prefer to see people use ln for natural log, Log for log base 10, and log for arbitrary logarithms.

 

But of course i wont get what i want.

[Dave]

I have to agree with matt on this one, although to be fair, it tends to be up to the author's preference. A lot of the more recent texts have started to adopt ln instead of log - personally, I prefer the latter because logs in an arbitrary base aren't as useful as the natural log and don't get used quite as frequently.

[matt grime]

No, you won't, since you are going against the notation used by a not unreasonable number of mathematicians - every one educated at Cambridge, not to mention every analyst I've ever met and so on. The only time logs are ever taken in *maths* (ie not physics or engineering) where base e is not the chosen base is log base 2 for use in coding theory. Of course that is guaranteed to have rebuttals, but I carefully qualify this as any reasonable mature treatment of analysis.

 

I must confess I have exactly one analysis textbook to hand, Goursat's classic text, and it uses log to mean base e, as would almost any other proper analysis book I@d be prepared to wager, and I've never seen ln used in complex analysis proper, writing as someone who's taken (several) graduate courses in (complex) analysis.

 

log is just the usual standard, johnny in *pure mathematics*, it is the only one that makes sense, just as radians are the only unit of angle that make sense really.

 

 

ln just signifies another dmbing down *sigh*, what next? Calling it the Argand plane?

[Johnny5]

No' date=' you won't, since you are going against the notation used by a not unreasonable number of mathematicians - every one educated at Cambridge, not to mention every analyst I've ever met and so on. The only time logs are ever taken in *maths* (ie not physics or engineering) where base e is not the chosen base is log base 2 for use in coding theory. Of course that is guaranteed to have rebuttals, but I carefully qualify this as any reasonable mature treatment of analysis.

 

I must confess I have exactly one analysis textbook to hand, Goursat's classic text, and it uses log to mean base e, as would almost any other proper analysis book I@d be prepared to wager, and I've never seen ln used in complex analysis proper, writing as someone who's taken (several) graduate courses in (complex) analysis.

 

log is just the usual standard, johnny in *pure mathematics*, it is the only one that makes sense, just as radians are the only unit of angle that make sense really.

 

 

ln just signifies another dmbing down *sigh*, what next? Calling it the Argand plane?[/quote']

 

Matt, it's not that important.

 

Here is Wolfram's discourse on natural log

 

They used ln there.

 

Here is wikipedia's article on natural logarithm

 

They mention both usages, but seem to favor ln.

 

Here is hyperphysics on natural logarithm.

 

They also used ln.

 

Here is Planet math on natural logarithm.

 

They used ln there.

 

Perhaps you went to Cambridge, I do not know. But I will say this... if going there helps you to know your stuff, then good.

 

Use either or... you will end up being followed.

 

Regards

[matt grime]

These places are, if you will, non-technical - they are not necessarily reflective of what happens in mathematics. Mathworld is from wolfram who are more applied than pure, wikipedia is written by the general public, presumably hyperphysics is written by physicists.

[Johnny5]

These places are, if you will, non-technical - they are not necessarily reflective of what happens in mathematics. Mathworld is from wolfram who are more applied than pure, wikipedia is written by the general public, presumably hyperphysics is written by physicists.

 

Speaking of hyperphysics, do you know who runs that site? It is seriously well organized.

 

I mean if i only read their whole site, I would learn a few things.

 

Do you know anything about who designed it?