In the last section we made note of the fact that exponential functions pass the horizontal line test and thus have an inverse.

YouTube Playlist: Logarithms and their Graphs

Using the steps for finding the inverse we obtain:

*y*. Therefore we make the following definition:

Use the proper terminology when reading logarithms,

reads “log base 5 of 125 is 3.” If given

then

*x*is called the argument of the logarithm. Also, notice that*y*is an exponent so the logarithm is actually an exponent, this will be important later.**Evaluate without using a calculator**.

**Instructional Video:**Introduction to Logarithms

The base

*b*can be any real number greater than zero but not including one - 10 and the natural base

*e*are used often.

A logarithm without a base is interpreted as the common logarithm.

**Evaluate using a calculator rounding off to the nearest thousandth**.

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