Lewis
2003-06-21 09:57:57 |
Log?
In some of the problems it has maths terms like 'log'. I'm only 13, so I don't know what that means. Perhaps there could be a page with different math terms and symbols, explaining what they mean for people like me. Or am I the only one? |
Cory Taylor
2003-06-21 13:46:39 |
Re: Log?
Lewis, a log can be explained as a measure of the order of magnitutde of a number. As the log gets larger, the number which it is derived from grows exponentially. To expand this idea into a strict definition, it is important to have a knowledge of exponents. For example, 2^5 or 10^3. If you don't understand this yet, then you'll need to figure this out first, as logs are simply an application of a particular relationship using exponents.
Logs can be of any "base", through there are two bases that are most prominent. When written as log, if there is no base mentioned (usually a number in brackets or subscript after the word log), then it is assumed to mean a base 10 log. If written as ln, it (always) means the base e log (e is an irrational number which is very important in Calculus. It's value is approximately 2.72). Now there are three parts to a log equation, and if you know two of them, with a little mathematical manipulation you can calculate the third.
a typical log equation is as shown log(10)100=2
The first part, the 10, is the "base". As Ive mentioned, if there is no mention of the base, and the equation is written "log" and not "ln", then you assume that the base is 10.
The second part is the number to which you are applying the log function, and the third is the "answer" to the log question. With a litttle experience, you will learn to see easily how these numbers are related, but to start out, the way that this log function is defined is as follows; the "base" of the log is the base of an exponential equation. The answer to the question is the exponent of the base, and the number which you were originaly logging is the answer to this modified expression. Following the example above, when you create an exponential expression with 10 as the base and 2 as the exponent, the result is 100. (10^2=100)
Remember that any number can be the base, it simply means that a little bit more complicated math results, for example
log(4)64=3, because 4^3=64.
With a little exposure to this system, you'll see that a number whose log (base 10) is one more than anothers, the first number is 10 times (because that is the base) greater than the first. For example if log x=34.115 and log y=35.115, then we know that y=10x.
Logs, while a difficult concept, are quite useful, especially in more advanced math. Here in Canada, we cover logs as curriculum around grade 10, so I would expect, Lewis, that this topic is not terribly far off in your scholastic endeavors.
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Gamer
2003-06-21 17:17:58 |
Re: Log?
Logarithmic scales are what I see them used for (like pH and such)... Think of a logarithmic scale like a normal scale, except multiplying instead of adding.
I can't tell you too much, am undereducated (at least relative to others) in math, but the way I always remembered it was "logs are exponents". |
Chris
2003-06-23 01:07:16 |
Re: Log?
Be concerned with logarithmic functions but not terrified; if you plan on pursueing a study in math, logarithmic functions will come around to get you. Consider a log as the inverse of an exponent, study their properties, ask questions when you are confused, and you should be ok. And don't forget repetition, repetition, repetition. If you wish, you may try entering the term "math" in a search engine on your computer and see the results. I have found a few helpful sites... |
TomM
2003-06-23 15:16:28 |
Logs and logarithmic scales
Since I seem to be older than most here, I'm not sure that any of you knew of them, much less remember them, but when I think of logs and logarithmic scales, i fondly remeber slide rules.
Slide rules were two piece "rulers" whose main scales (labelled for some arcane reason the "C" and "D" scales) were used to multiply large numbers. Other scales performed other operations. (This was before calculators became handheld and "scientific" calculators became affordable.)
You can see the way two ruler scales can be used to perform a binary operation by using two ordinary rulers to perform addition. Say you want to add 5 + 2. Slide the first ruler so that the "zero point" is aligned with the "5" on the second ruler. Then find the "2" on the first ruler. The marking ("7") on the second ruler next to that "2" is the result you are seeking. (2 inches beyond 5 inches is 7 inches.)
A slide rule's "C" and "D" scales were marked, not in linear distance, but in the "common log" (base 10 log) of that distance. It worked because (10^a)(10^b) = 10^(a+b), which also means that log(A) + log(B) = log(AB), so you were adding the logs the same way you added inches in my last paragraph.
Here are some sites about logarithms:
http://www.sosmath.com/algebra/logs/log1/log1.html
http://www.sosmath.com/algebra/logs/log4/log44/log44.html
http://www.physics.uoguelph.ca/tutorials/LOG/
And some about slide rules:
http://www.sphere.bc.ca/test/sruniverse.html
http://www.hpmuseum.org/srinst.htm
http://www.eminent.demon.co.uk/sliderul.htm
http://www.dotpoint.com/xnumber/hp.htm
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levik
2003-06-24 07:40:18 |
Re: Log?
Heh - I remember those from when I was a kid. My parents had a whole bunch from their college days.
They weren't really using them anymore, so I was allowed to play with them - I always thought the sliding center was a lot of fun.
Needless to say, I never did figure out how to use the darn things. |
Lewis
2003-06-24 08:19:18 |
Re: Log?
Thanks for all your help guys, I appreciate it.
I'm currently reviewing the websites TomM mentioned, so (hopefully) next time I come on I'll be able to solve problems like 'A Couple of Logs'. :) |
allan
2004-02-16 21:12:48 |
Exponent more than 100
How to solve a problem with the exponent of more than 100?
e.g
156 with exponent 100
how to solve it
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Gamer
2004-02-17 19:02:10 |
Re: Log?
You can always tell a computer to do it, or do it by hand. I don't know that there's any other super way. There's other ways to tell things about it, but if you just want to know the whole big long number you will be stuck. |
