SOLUTION: Billy is graphing f(x) = log base 4 (2x-3) + 1 without a calculator. Name two points he could use on his graph if both points can only have y-coordinates that are integers. Show al

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Billy is graphing f(x) = log base 4 (2x-3) + 1 without a calculator. Name two points he could use on his graph if both points can only have y-coordinates that are integers. Show al      Log On


   

Question 1115169: Billy is graphing f(x) = log base 4 (2x-3) + 1 without a calculator. Name two points he could use on his graph if both points can only have y-coordinates that are integers. Show all work.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


If log%284%2C2x-3%29%2B1 is to be an integer, then log%284%2C2x-3%29 must be an integer.

That means 2x-3 must be a integer power of 4.

Some choices....
4%5E0=1; 2x-3=1 --> x = 2. log%284%2C2x-3%29%2B1+=+log%284%2C1%29%2B1+=+0%2B1+=+1 --> (x,y) = (2,1)
4%5E1=4; 2x-3=4 --> x = 7/2. log%284%2C2x-3%29%2B1+=+log%284%2C4%29%2B1+=+1%2B1+=+2 --> (x,y) = (7/2,2)
4%5E2=16; 2x-3=16 --> x = 19/2. log%284%2C2x-3%29%2B1+=+log%284%2C16%29%2B1+=+2%2B1+=+3 --> (x,y) = (19/2,3)

etc., etc....