Aces High Bulletin Board
General Forums => The O' Club => Topic started by: midnight Target on September 15, 2003, 08:14:49 AM
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Logarithms... Back in my day there were "natural logs" based on a number like 2.?????????. What the heck are these used for, and where did that number come from?
Always wondered.
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Growth and decay, interest rates, mortgage, population growth... one use: P = e^kt
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Thanks
Doesn't explain the number though.
For example 3.141... is the ratio of the diameter to the circumfrence of a circle. Where the heck did 'e' come from?
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The main use of logarithms was to torture poor unfortunates such as myself. To multiply two numbers together, you would would look up the logarithm value for each in a book, then add those values together. Then, you would look up the result of that addition in the antilogarithm chart to get your decimal answer. I seem to remember something about "bar one", in a value like 1.08 - which meant that the 1 was negative but the .08 was still positive. All very confusing, and of doubtful use in the modern age.
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2.7..... is special number. When you differentiate exp(x) you get .... exp(x) daaa daaa (where exp is the base of a natural log). This makes them convienient to work with. They can also give rise to hyperbolic and trigonemetric functions.
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PH scale is a logarithm. So is the decibel scale.
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:mad:
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MT - I remember now.
The log values represent 10 to the power n - so the log value for 100 is 2 because 100 is 10². The log value for 1000 is 3 because 1000 is 10³.
The log value for 1 is zero because any number to the power zero is 1. Any number to the first power is itself.
Now all we have to do is to find a use for all this...
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Originally posted by davidpt40
PH scale is a logarithm. So is the decibel scale.
And Richter..
niknak.. thats the info I'm looking for, the 2.7???? - Why 2.7????
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The circumference of a circle is approximately 3.141 times the diameter. This special value is known as pi. (a letter in the Greek alphabet)
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logarithms right after reading the morning comics :)
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Originally posted by Eagler
logarithms right after reading the morning comics :)
LOL Eagler. At least you don't try to polish 'em. :D
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An mathmetician will tell you that it is impossible to pick up an object. In order to pick it up, you must first walk halfway there. Then halfway again from the other half you just walked, and so on. According to this logic, you'll never arrive at the object in order to pick it up.
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Originally posted by beet1e
MT - I remember now.
The log values represent 10 to the power n - so the log value for 100 is 2 because 100 is 10². The log value for 1000 is 3 because 1000 is 10³.
The log value for 1 is zero because any number to the power zero is 1. Any number to the first power is itself.
Now all we have to do is to find a use for all this...
Well done beetle...
Now go get a gun and shoot your reading comprehension teacher.
I know what a logarithm is. I'm wondering where the base number for natural logs comes from.
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Originally posted by GrimCO
An mathmetician will tell you that it is impossible to pick up an object. In order to pick it up, you must first walk halfway there. Then halfway again from the other half you just walked, and so on. According to this logic, you'll never arrive at the object in order to pick it up.
Zeno's paradox.
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e comes from evaluating the expression (1 + 1/n)^n
As n gets larger and larger, it starts to get closer and closer to the value of e (which truly can't be reached exactly, since e is an irrational number).
Simple table showing what I am talking about:
n (1 + 1/n)^n
100 2.70481
1000 2.71692
100000 2.71827
1000000 2.71828
and so on...
e is used quite a bit in calculus and comes up in mathematical theory and in applications (pretty much anything that uses calculus as a base, i.e. engineering and physics).
As far as the half the distance thing mentioned by Grim:
Yes, in theory, you won't reach the object. But I haven't ever met a mathematician that says you would never actually reach it. The half the distance theory is only truly applicable when both the thing moving and the destination occupy no space. Basically, it means the two things are points.
But, as you and everyone else are aware, this is not the case in the real world. It is an interesting topic of discussion in math classes, but that is about it.
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Originally posted by midnight Target
Now go get a gun and shoot your reading comprehension teacher.
LOL - probably already dead. Sorry, but I didn't know about these "natural logs" that you speak of...
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(1 + 1/n)^n
Thank you Mathman, exactly what I was looking for.
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ARRRGGGGHHH my ****ing eyes!!!!! AAHHHHHHHH
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LOL...
make the bad symbols go away!!
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Originally posted by midnight Target
Thank you Mathman, exactly what I was looking for.
e was discovered by Euler, one of the greatest mathematicians in history.
e is derived from computing and interest on a loan. Typically you pay say 5% interest a year, but you can compute it monthly, weelky, daily etc. For example for a monthly computation, you are paying 5%/12 interest each month. that's where (1 + 1/n)^n comes from.
e comes from calculating an interest continually, the interest calculation interval goes to a zero.
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I made 2.71 natural logs this morning.
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:D
how did you measure it?
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Just count the splashes.
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better than a spray, I suppose.......
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Originally posted by FUNKED1
Just count the splashes.
Havana omelette?
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Originally posted by mietla
e was discovered by Euler, one of the greatest mathematicians in history. .
thought e was discovered by Bay :)
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Originally posted by midnight Target
LOL...
make the bad symbols go away!!
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Mathman... you rock.
Can you give me some insight on the following?
y = xe^x
and solve for x? Looks doable at first, at least it did to me. :)
I busted my head on that one for a long time before finding a solution on the internet, and the solution involved a "function" that I had never seen before. I totally forget what it was, too. :)
Anyway, I'm curious if there's some significance to the above equation or its solution...
Kekule
WB: 18th Sentai
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If you haven't heard Tom Lehrer's 'New Math' song, it's quite entertaining. He dissects the concept of new math quite viciously.
Examples:
"...In the new approach, the important thing is to understand what you're doing, not to get the right answer"
"The book I got this problem out of wants you to do it in base 8, but don't panic. Base 8 is just like base 10 really.... if you're missing two fingers."
Lyrics:
http://www.lyricsfreak.com/t/tom-lehrer/138395.html
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Originally posted by GrimCO
An mathmetician will tell you that it is impossible to pick up an object. In order to pick it up, you must first walk halfway there. Then halfway again from the other half you just walked, and so on. According to this logic, you'll never arrive at the object in order to pick it up.
hehe, funny but faulty logic. To pick up an object you must first walk all the way there, not half. :)
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At a quick glance i am fairly sure you cannot put xe^x in the form
x= .....
the e^x and the x are not reconcilable.
You could turn it into a differential equation -> y' - y - e^x = 0 but this does not really help!?!
I could however be wrong, it has been known to happen once or twice (an hour).