Problem:
For all positive integers n, let f(n)=log2002​n2. Let
N=f(11)+f(13)+f(14)
Which of the following relations is true?
Answer Choices:
A. N>1
B. N=1
C. 1<N<2
D. N=2
E. N>2
Solution:
We have
N=log2002​112+log2002​132+log2002​142=log2002​112⋅132⋅142=log2002​(11⋅13⋅1
Simplifying gives
N=log2002​(11⋅13⋅14)2=log2002​20022=2​
The problems on this page are the property of the MAA's American Mathematics Competitions