1
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We're asked to convert 10 to the second power,

2
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or 10 squared, equals 100 into a logarithmic equation.

3
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Now this is saying, if I take base 10-- so I'll do 10 in yellow --

4
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I take the base 10 to the exponent 2, then I get 100.

5
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When you do a logarithm, it is really kind of the inverse of that,

6
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it is really kind of the other way of thinking about it.

7
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A logarithm says: "what power do I have to raise the base to, to get 100?"

8
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So if I were to write log, base 10, of 100-- and I wrote the ten a little bit bigger than is typically done,

9
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let me write it this way-- log base 10 of 100, this says

10
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what power do I have to raise 10 to, my base, to get 100?

11
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And we know from this, and probably you knew this even if we didn't have this written down,

12
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you would have to raise it to the second power.

13
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So this is equal to 2.

14
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So right over here we are saying in an exponential equation, the base ten, to the second power

15
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is equal to 100. Here in the logarithmic equation we are

16
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saying that the power that we have to raise 10 to to get 100 is equal to 2.

17
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So these are really saying the exact same thing.

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And just so you get the terminology right, this, in both cases,

19
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the ten is referred to as the base, this is the base,

20
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and in both cases the 2, -- let me write it--

21
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so in both cases the 2 is referred to, and I think you know this already, as the exponent.

22
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And then the 100 is what you get when you raise the base to the exponent.

23
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So these are two ways of writing the exact same truth about 10 to the second power equaling 100.