Find an equation with the form below with a, b, c being integers

Question

Find an equation of the form y=c+b log_ax with a, b, and c being the integers whose graph contains the two points: (4,10) and (2,12) 

Answer 1

There are three unknowns, a, b & c but just two equations. If we let a=10 (integer value & therefore using common logs) then

12 = c  +b•log2

10 = c + b•log4

 

then 2 = b(log2 - log 4) and then you could solve for b but it would not be an integer.

But if a=2, then log_a 2 = 1 and log_a 4 = 2, so let's try this.

 

12 = c + b

10 = c + 2b

 

then -2 = b and c = 14.  My solution: (a,b,c) =(2,-2,14)