Problem:
Points A and B lie on the graph of y=log2​x. 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,log2​r) and (s,log2​s) be the coordinates of points A and B, respectively, and assume r<s. The midpoint of AB is
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​​.
