Problem:
The set of all real numbers x for which
log2004(log2003(log2002(log2001x)))
is defined as {x∣x>c}. What is the value of c ?
Answer Choices:
A. 0
B. 20012002
C. 20022003
D. 20032004
E. 200120022003
Solution:
The given expression is de ned if and only if
log2003(log2002(log2001x))>0
that is, if and only if
log2002(log2001x)>20030=1
This inequality in turn is satis ed if and only if
log2001x>2002
that is, if and only if x>20012002.
The problems on this page are the property of the MAA's American Mathematics Competitions