Logarithmic and Exponential Functions - Inverses

1. Logarithmic and Exponential Functions - Inverses • Recall an important property of inverse functions: the composite of the functions is x. If we assume that functions f and g are inverses of each other, then ... • Since the exponential and logarithmic functions are inverses of each other, their composites result in x.

2. Logarithmic and Exponential Functions - Inverses • Let exponential and logarithmic functions be given by: • Form the composite of f with g: • Using the inverse property discussed earlier, this means ... • Note that for the exponential and the logarithm, the bases are the same real number b. Slide 2

3. Example 1: Simplify Logarithmic and Exponential Functions - Inverses Since this is the composite of an exponential function and a logarithmic function, each with a base of 3, the result is ... Slide 3

4. Logarithmic and Exponential Functions - Inverses • Example 2: Simplify Slide 4

5. Logarithmic and Exponential Functions - Inverses • Note the use of the inverse property in the next to last step where ... Slide 5

6. Logarithmic and Exponential Functions - Inverses • Let exponential and logarithmic functions be given by: • Now form the composite of g with f: • Using the inverse property g(f(x)) = x, this means ... • Note that for the logarithm and the exponential, the bases are the same real number b. Slide 6

7. Example 3: Simplify Logarithmic and Exponential Functions - Inverses Since this is the composite of a logarithmic function and an exponential function, each with a base of 4, the result is ... Slide 7

8. Logarithmic and Exponential Functions - Inverses • Example 4: Simplify • Note the use of the inverse property in the last step where ... Slide 8

9. Logarithmic and Exponential Functions - Inverses END OF PRESENTATION Click to rerun the slideshow.