Find an equation of the form

Question

y=c+blog_ax with a, b, c being integers whose graph contains the two points: (1,1) and (5,7)

Answer 1

y = c + b·log_a(x)

 

First, plug in (1,1) for the x and y values:

 

     y = c + b·log_a(x)

     1 = c + b·log_a(1)

 

Since log_a(1) = 0 for any base, we get 1 = c.  Now plug in the second point, (5,7):

 

     y = c + b·log_a(x)

     7 = 1 + b·log_a(5)

     6 = b·log_a(5)

 

Choose a = 5, since log₅(5) = 1:

 

     6 = b·log₅(5)

     6 = b·1

     6 = b

 

So we have a = 5, b = 6, c = 1.  The final equation is:

 

     y = 1 + 6·log₅(x)