logs - here are a couple of special logarithms that arise...

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here are a couple of special logarithms that arise in many places. These are, In the natural logarithm the base e is the same number as in the natural exponential logarithm that we saw in the last section . Here is a sketch of both of these logarithms. From this graph we can get a couple of very nice properties about the natural logarithm that we will use many times in this and later Calculus courses. Let’s take a look at a couple of more logarithm evaluations. Some of which deal with the natural or common logarithm and some of which don’t. Example 2 Without a calculator give the exact value of each of the following logarithms. (a)

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(b) (c) (d) (e) Solution These work exactly the same as previous example so we won’t put in too many details. (a) (b) (c) (d) (e) This last set of examples leads us to some of the basic properties of logarithms. Properties 1. The domain of the logarithm function is . In other words, we can only plug positive numbers into a logarithm! We can’t plug in zero or a negative number.
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