Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Quantumcat on 28/11/2003 07:20:16
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I have to do an assignment on some guy called Napier, one of the things he did was invent logarithms I think, and I have to explain what they are and how they work >_< never seen a log in my life until now. By reading a website I have figured out (yay) that x (exponent) = log b (base) y (power) but I don't know what you're meant to do with them. If anyone knows a good website that explains them properly in detail or can explain them themselves that'd be really cool. Thanks.
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Angel will know, she is good at maths. I will learn log and exponential soon as well. (Not for a couple of months)
Tom
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Wikipedia has a pretty good logarithm entry:
http://en.wikipedia.org/wiki/Logarithm
Logs are confusing at first, but they boil down to just an algrebraic method for finding unknowns that are part of exponents. Purely academic exercised aside, they're used quite extensively in science and engineering for solving differential equations. (like for carbon-14 dating, bacterial growth rates, heating/cooling functions, etc)
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The reason they are used to solve differential equations is that the differential of a natural log function is a natural log function. It makes the equations easier, and an amazing number of natural processes are very well modeled by natural log functions. Things like cannibinoid was talking about - radioactive decay, population growth rates, heat transfer, capacitor charging/discharging to name a few.
Base ten logs were used before calculators were invented (yes, there was such a time) because multiplication and division become addition and subtraction after you take the log of the numbers in question. Then you take the inverse log of the result to get the answer.
Not an explanation, but a little more real world.
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John
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Didn't slide rules use logarithmic properties to perform mathematical functions (multiply, divide, exponent, etc) on big numbers? Or were they just for solving log functions? I'm just a young'in, these things are before my time. My phys. chem. professor brought one into class the other day to taunt us with...he may as well have brought in an abacus.
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Yup, slide rules used the properties of adding and subtracting logs to do multiplication and division of numbers. I don't know how to use one, but I've had a couple of lessons. I've known someone who was really good with one and could work problems faster with his SR than I could with a calculator. Of course he was limited to three or four significant figures because of the resolution of the marks on the SR. That is enough in most engineering calculations, at least until you start doing orbital mechanics. hi dadi
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John