Problem:
A circle has a radius of log10​(a2) and a circumference of log10​(b4). What is loga​b?
Answer Choices:
A. 4π1​
B. π1​
C. π
D. 2Ï€
E. 102Ï€
Solution:
The given information implies that 2πlog10​(a2)=log10​(b4) or, equivalently, that 4πlog10​a=4log10​b. Thus
loga​b=log10​alog10​b​=π​
The problems on this page are the property of the MAA's American Mathematics Competitions