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Can someone explain logarithms?

Seeing all of the other math Instructables on here, I was surprised not see one on logarithms. I just want to learn beyond my mundane curriculum. Thanks.

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kelseymh7 years ago
Cameron's response below gives you a good definition of a logarithm: logb(N) is that number which, when used to exponentiate b, gives you N. However, I think you're asking, "what are logarithms good for?" Nowadays, not much unless you are a physicist specializing in either thermodynamics or QCD.

In the old days, before calculators, logarithms were a way to allow you to do fairly complex arithmetic with nothing but addition and subtraction. For multiplication, there is a rule for exponents: bx×by = bx+y. So if you have two numbers N and M which you want to multiply, then you can look up the logarithms, and use log(N)+log(M) = log(N×M). Similarly, for division you have bx/by = bx-y, and you can use log(N)-log(M) = log(N/M). If you have some complex calculation, you can do everything in terms of logs, and only look up the exponential ("inverse log") at the very end.
then you can look up the logarithms

hee hee, log tables....
Yeah, yeah, I should have used the past tense. I'm pretty sure even the CRC Handbook has dropped their log tables by now.
In the old days, before calculators, logarithms were a way to allow you to do fairly complex arithmetic with nothing but addition and subtraction.

In a very real sense, you can't really do anything to a number except add to it or subtract from it. The rest of math is just fast and fancy ways of doing this.
That is true of real numbers. In the complex plane, you can rotate a number without adding or subtracting anything; and don't get me started about quarterions.

I'm not fully convinced that your statement is universally correct. Consider the operation of raising to a non-integer power (which is the whole point of logs, after all). Integer powers are equivalent to multiplication (n3 = n×n×n), and multiplication is equivalent to repeated addition.

But if you raise a number to a floating-point power, how do you break that down into addition and subtraction, without invoking some more complex operation to deal with the fractional part?
If you want enrich your  "multiplication is equivalent to repeated addition" comment, go to:

The “Multiplication is Not Repeated Addition” Research:
http://numberwarrior.wordpress.com/2009/05/22/the-multiplication-is-not-repeated-addition-research/

and

“Multiplication is Not Repeated Addition” Revisited:
http://numberwarrior.wordpress.com/2010/02/26/multiplication-is-not-repeated-addition-revisited/
Ockham's razor
Pardon?
Oops, I was answering Kelseymh, about the simplest way to frame the statement. :-)
Oh, OK!
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