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Functions.Logarithms.SocialMedia.idf.UtilityOfMoney_ITI_111.2011S.doc. - 1 - 1. Speaking Mathematics Today's class is going to begin with a very very very important digression from the mainstream of learning about the mathematics of searching. As you know, from time to time we wander around the class looking over your shoulders to see what you're writing in your notebooks. And a few years ago we realized that something horrifying was happening. We realize that when we write something on the board like x to the power 2, just as I've written here ( 2 x )and then we look in your notebooks we see all kinds of strange things like X2 or maybe even X with a subscript 2. And that was kind of puzzling because you can all see what's here on the board. But we learned that the problem is in human psychology. When you see something, most of you say it to yourselves. And then you go and you write down what you just said. So if you're looking at the board and what you say to yourself is “x two” then you're going to write down “x two” looking like this: x2. And what happens then? What happens is that when you go to study your notes absolute confusion reigns. So to help you all get an A (well, maybe a B+) in this course we have just got to spend some time now practicing saying mathematical expressions. [And along the way we will sneak in some nifty new ideas, and talk about happiness.] 1.1. Pronouncing exponents For example, this one is “X to the fifth power” or “X to the power five”. [ 5 x ] But this one is “five X” or you might say “five times X”. . And this one is “five by X” or “five over X” or if you want to be really fancy. “five divided by X”. [ 5/ x ] Here's a little more complicated one. Let's all pronounce it together. “Four a, plus five b, all over c”. (4 5 ) / a b c Here is a another one to pronounce. “x to the power a time x to the power b”. Here is “ X to the power A+ B”. Of course you have to kind of read that with parentheses because this other thing would also be pronounced “X to the power A, plus B”. Sometimes to make it really secure we say that the first one is “X raised to the power A plus B [pronounced in a rush]”.
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Functions.Logarithms.SocialMedia.idf.UtilityOfMoney_ITI_111.2011S.doc. - 2 - Here are some other ones for you to pronounce. “x squred times x cubed”. Or “x tothepower 3 time x to the power 2” “x to the fith”. “a to the power six”. “b to the power minus three” or “b to the negative three”. I will come back to these little bit because we're actually talk about exponents in this class. 1.2. Working with exponents Let’s interrupt our language lessons for a little while here and talk about what all this means. The expression “x to the power a” means “x multiplied by itself a times”. So 1 x means x. A nd 2 x xx . Now [see illustration] ab x multiplied by itself a times, and then b times, for a total of (a+b) times. So () a b a b x x x .
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This note was uploaded on 02/20/2012 for the course 790 373 taught by Professor Boros during the Fall '09 term at Rutgers.

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