Problem:
How many zeros does f(x)=cos(log(x)) have on the interval 0<x<1?
Answer Choices:
A. 0
B. 1
C. 2
D. 10
E. infinitely many
Solution:
Note that the range of logx on the interval (0,1) is the set of all negative numbers, infinitely many of which are zeros of the cosine function. In fact, since cos(x)=0 for all x of the form 2π±nπ,