Question

What is the relationship between exponents and logarithms? How would you
distinguish between the two, using both a graph and a sequence?

Answer 1

logarithms are an expression that tell you what the exponent is. For example, log base 2(8) = 3 because 2^3 = 8. In order to graph a log, you have to turn it into an exponential form. Usually logs are written and used as bases 10 or the number e. When e is used it is called the natural log. They all follow the graphs of exponential functions and change according to the numbers they are attached to. With a sequence things are a little more tricky, and you need some good know how to really tackle alot of that stuff. It's fun to get to know if you're into math like that, but to be honest I'm still not a complete pro at alot of it because there are alot of things to remember, and I'm more into some other concepts that really don't require me to expand functions in series and stuff like that for the time being. Pretty soon I'll be back on it for about the 3rd or 4th time, because I need it for diff eqs. and some physics stuff. Just know that you can expand an exponential function into an infinite series, consider the partial sums of that series and get results. It's really tight, but takes quite a bit, because there are different forms, rules and tests for dealing with series. It's worth getting to know, but keep in mind, they have college classes devoted just to that topic, and analysis based on it.