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à  EXPONENTS: The exponential function f with base a is denoted by f(x) = ax,                         

                                   where a>0, a ≠ 1, and x is any real number.

 

 

Exponential Form: x = ay

 

 

à  e ~ 2.71828

 

 

à  THE NATURAL BASE e

            For many applications, the convenient choice for a base is the irrational number

        e ~ 271828, the natural base

 

      The function f(x)=ex is the natural exponential function

 

Exponential equation: ex= 72

                                 lnex= ln72

                                     x= ln72

                                     x~ 4.277

   

      The equations y= logax and x=ay are equivalent

 

à EVALUATING EXPONENTIAL FUNCTIONS

 

1. x= log47                   2. log232=5                  3. log107=.845

  4x = 7                                   25=32                     10.845=30

 



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