Module 6: Lesson 3

 

Self-Check 4

3. Question 16 on page 381 of the textbook
   
   16. Given that the equation is f(x) = logc x and that a point on this function is , substitution gives the following:
       
       
        
       
       
       Rearranging into exponential form and solving for c gives the following:
       
       
        
       
       
       At this point, this question can be solved in two ways.
       
       The point (4, k) can be substituted into the inverse equation of f(x). To determine the inverse of f(x) = log2 x or y = log2 x, switch the x- and y-variables to become x = log2 y. Next change to exponential form: y = 2x or f −1(x) = 2x. Substitute (4, k) into f −1(x) = 2x.
       
       
        
       
       
       

       Or, the inverse of the given point, in this case (k, 4), can be substituted into the original equation.
       
       

        
       
       
       

       Thus, the value of k is 16.

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