6.3 Differentiation and Integration of Logarithmic and Exponential Functions
6.2 Exponential and Logarithmic Functions
Learning Objectives
A student will be able to:
- Understand and use the basic definitions of exponential and logarithmic functions and how they are related
algebraically. - Distinguish between an exponential and logarithmic functions graphically.
A Quick Algebraic Review of Exponential and Logarithmic Functions
Exponential Functions
Recall from algebra that an exponential function is a function that has a constant base and a variable exponent. A
function of the formf(x) =bxwherebis a constant andb>0 andb 6 =1 is called an exponential function with base
b.Some examples aref(x) = 2 x,f(x) =(^12 )x,andf(x) =ex.All exponential functions are continuous and their
graph is one of the two basic shapes, depending on whether 0<b<1 orb> 1 .The graph below shows the two
basic shapes:
Logarithmic Functions
Recall from your previous courses in algebra that a logarithm is an exponent. If the baseb>0 andb 6 = 1 ,then for
any value ofx> 0 ,the logarithm to the basebof the value ofxis denoted by
y=logbx.