Problem:
Square ABCD has area 36 , and AB is parallel to the x-axis. Vertices A,B, and C are on the graphs of y=logax,y=2logax, and y=3logax, respectively. What is a?
Answer Choices:
A. 63
B. 3
C. 36
D. 6
E. 6 Solution:
Let A=(p,logap) and B=(q,2logaq). Then AB=6=∣p−q∣. Because AB is horizontal, logap=2logaq=logaq2, so p=q2. Thus ∣∣∣q2−q∣∣∣=6, and the only positive solution is q=3. Note that C=(q,3logaq), so BC=6=logaq, from which a6=q=3 and a=63.