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Use a calcuator to find log base e of 67 to the nearest thousandth

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So just as a reminder, e is one of these crazy numbers that shows up

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in natures and finance and all these things and it is approximately equal to 2.71 and it just keeps on and on

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so you could view log

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base is as 67 and you say "What does 'e' mean?" Well, e is just a number

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just like pi is just a number

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This is really the same thing as saying log base 2.71 and teh actual number

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so you have to write all the digits that just keep on going forever

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and never repeat- of 67. So what power do I have to raise e to

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to get to 67? So another way of saying that is that if this is

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equal to x, e to the x is equal to 67, we need to figure out what x is

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Now, traditionally, you will never see people write log base e even though

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e is one of the most common bases to take a log of

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so the reason you wouldn't see log base e written this way

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is that log base e is the natural logarithm

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and I think that's used because e shows up so many times in nature.

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So log base e of 67, another way of saying that- or seeing that- and the more typical

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way of seeing that is the natural log. This is ln (I think this is from french or something)

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So this is the same thing as saying log base e

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of 67. This is saying that exact same thing.

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So what power do I have to raise e to to get 67. When you see this 'ln', is literally means

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'log base e'. Now, they let us use a calculator and that's good

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because I don't know off the top of my head what power you

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have to raise 2.71 and so forth to to get 67.

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So we'll get our calculator out. So we'll get our TI-85 out.

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And different calculators will have different ways of doing it.

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If you have a graphing calulator like this, you can literally type in the

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statement, natural log of 67 and evaluate it.

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So here, this is the button for natural log, 'log naturale (fr),' maybe.

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Ln of 67, and then you press 'enter' and it will give you the answer.

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If you don't have a graphing calculator, you might have to press 67

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and then press 'ln' to give you the answer. But if you have

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a graphing calculator you can jsut type it in the same

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way as you would write it out.

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So 4.20469... and we want to roud to the nearest thousandth.

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So this is the thousandth place, this 4, the digit after that is 5

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or larger, it's a 6, so we are going to round up.

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So this is approximately equal to 4.205

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and it actualy makes a lot of sense, because we know that e is greater than 2

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and it is less than 3

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and if you think about 2 to the 4th power, that gets you to 16

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and 3 to the fourth power gets you to 81.

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67 is between 16 and 81, and e is between 2 and 3

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so at least if feels right

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that 2.71^4 should get you pretty close to 3^4.