Problem:
A circle has a radius of log10β(a2) and a circumference of log10β(b4). What is logaβb?
Answer Choices:
A. 4Ο1β
B. Ο1β
C. Ο
D. 2Ο
E. 102Ο
Solution:
The given information implies that 2Οlog10β(a2)=log10β(b4) or, equivalently, that 4Οlog10βa=4log10βb. Thus
logaβb=log10βalog10βbβ=Οβ
The problems on this page are the property of the MAA's American Mathematics Competitions