Example Sketch the graph of the common logarithm & the natural logarithm on the similar axis system.

Solution

This instance has two points.  Firstly, it will familiarize us to the graphs of the two logarithms that we are most likely to illustrate in other classes.  Also, it will provide us some practice by using our calculator to evaluate these logarithms since the reality is that is how we will require doing most of these evaluations.

Following is a table of values for the two logarithms.

Following is a sketch of the graphs of these two functions.

Now let's begin looking at some properties of logarithms.  We'll begin with some fundamental evaluation properties.