Date: 01/29/98 at 11:00:58 From: Brad Edey Subject: The 'log' button In math we have been using the 'log' button on our calculators to solve problems that involve compound interest, etc., and our teacher says we'll learn what the 'log' button does next year. But we want to know now! The teacher says it has something to do with the opposite of exponents, but I still have no clue.
Date: 01/29/98 at 15:23:30 From: Doctor Sam Subject: Re: The 'log' button Well, logarithms can be a big topic and if you are interested you might try reading about them in another math book. But for a quick introduction, here goes: First, the word logarithm is really a synonym for the word exponent or power. Second, there are lots of different kinds of logarithms depending upon the base you are using. The LOG key on your calculator is probably "base 10 logarithm". Try this: make a table of values of different powers of 10, like this: power x: -2 -1 0 1 2 3 ... 10^x 0.01 0.1 1 10 100 1000 ... Ordinarily we read these as "10 to the power 2 equals 100" or "10 to the power 3 equals 1000." This is fine when you need to calculate a power of ten, but what if you know the answer and need to find the exponent? To solve 10^x = 10000, for example, you have to think "ten to what power is ten thousand?" That's not too hard. But what if the problem is 10^x = 25? LOGARITHMS were invented (back in the sixteenth century I think) to answer these kinds of questions. LOG (25) means "the power of 10 that produces 25" and LOG(1000) = 4 because "the power of 10 that produces 1000 is 4." You can make a little table of logarithms just by switching the two rows of my table above: 10^x 0.01 0.1 1 10 100 1000 ... power x: -2 -1 0 1 2 3 ... only now the second row is called the logarithm. So here it is one more time: n 0.01 0.1 1 10 100 1000 ... LOG(n): -2 -1 0 1 2 3 ... Back in the sixteen hundreds (in fact even back in the dark ages when I went to school in the 1960's) we didn't have pocket calculators with LOG keys. Companies published books of tables, page after page of the powers of 10 that would give you almost any number you wanted. It's a lot easier to press a key! I do want to mention that the little table I used gives powers of 10, and so these are called base ten logarithms (or COMMON LOGARITHMS). But almost any number can be used as the base. If you are interested in solving problems with powers of 2 (175 = 2^x) it would be helpful to have a base two logarithm key on your calculator. You probably don't have one, but computer scientists who use powers of two a lot do. I hope that helps... -Doctor Sam, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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