How to graph Logarithmic Functions

Ok, while reading through some of my classmates' blogs, I realized that some don't know how to graph log functions. So here is my guide on how to do so.

Graphing average Logarithmic Functions (this means a log function without transformations): First, know how the general graph of an exponential function looks like, as it will come into play later. Ok, first you will need 2 or 3 points (this is for general logarithmic functions without transformations). One of these points is going to be (1,0) because anything taken to the power of 0 is 1 (if you don't believe this is a point, test it yourself). The second point is going to be (x,1), where is x is the base (the base taken to the first power is itself). The third point is (x,2), where x in this case is the base taken to the second power (if you have any doubts on these points, test them yourself). These 2 or three points should tell you what one part of the graph is going to look like. Now for the part of the graph involving fractions. If you know what the general exponential function looks like and know that logarithmic functions are simply exponential functions reflected across the line of y=x, then you might be able to figure out what the part of the graph looks like where x is a fraction. If you can't do so, as x is a fraction and the fraction gets smaller, the graph will get closer and closer to the y-axis (line x=0), but never actually touch it (if you can't visualize this, test fractions into logarithmic functions and you will see very soon what I mean). In the end, it should look like its exponential counterpart reflected across the line y=x (if you need more points than those suggested above, plot as many points you need until you yourself can see what the graph looks like).

Graphing the Natural Log: If you are graphing the natural log, f(x)=ln x, don't panic. It is not as different from graphing a logarithmic function because it is one as well. All you need to know is that the base is e which approximates to 2.71828282.... or something along those lines (please check the actual value yourself just to be sure). (1,0) is still a point, (e,1) becomes one point, and (e^2,2) becomes the next point. Then, create the general graph by connecting the dots with a curve (for the part of the graph where x is a fraction, see my above explanation). For the actual values of e and e^2, please use a calculator and approximate on the graph there positions. Again, nothing too hard.

Logarithmic Functions with Transformations: I have no trick to these. The only advice I can offer is to take the transformations slowly and one step at a time.

This is pretty much how it's done. If you have your own special method for graphing these, by all means do so, this is for those having difficulties. I hope this helps all of you who are struggling with graphing.