Problem:
Points A and B lie on the graph of y=log2x. The midpoint of AB is (6,2). What is the positive difference between the x-coordinates of A and B?
Answer Choices:
A. 211
B. 43
C. 8
D. 45
E. 9
Solution:
Let (r,log2r) and (s,log2s) be the coordinates of points A and B, respectively, and assume r<s. The midpoint of AB is
(2r+s,2log2r+log2s)=(2r+s,log2rs).
Setting this equal to (6,2) yields the system of equations r+s=12 and rs=16. This means r=6−25 and s=6+25, so the requested difference is (D)45.
