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

Question

i am struggling with this section an could use a bit oh help thank you

Answer 1

Logs and exponents of the same base are inverse functions of one another.  Imagine an exponent machine that takes x as an input as produces a^x as an output.  A Log machine would take that a^x as an input and produce the original x back as the output.  So the log "undoes" what the exponent does.

 

x -->[Exponent] --> a^x -->[  Log_a ] --> x                   log_a(a^x) = x

           (base a)                     (base a)

 

It work the other way as well - the Exponent function undoes what the Log function does to x:

 

x -->[   Log_a   ] --> log_a(x) -->[Exponent ] --> x        a^log_a(x) = x
         (base a)                             (base a)

 

To see representative graphs, click on the link below:

 

http://www.wyzant.com/resources/files/290591/log_and_exponent_graphs

 

For a good general overview of the relation of exponents and logs, click on the link below:

 

http://www.purplemath.com/modules/logs.htm