Difference between revisions of "2004 AMC 12A Problems/Problem 16"
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<cmath>\log_{2004}(\log_{2003}(\log_{2002}(\log_{2001}{x})))</cmath> | <cmath>\log_{2004}(\log_{2003}(\log_{2002}(\log_{2001}{x})))</cmath> | ||
| − | is defined is <math>\{x | + | is defined is <math>\{x\mid x > c\}</math>. What is the value of <math>c</math>? |
<math>\textbf {(A) } 0\qquad \textbf {(B) }2001^{2002} \qquad \textbf {(C) }2002^{2003} \qquad \textbf {(D) }2003^{2004} \qquad \textbf {(E) }2001^{2002^{2003}}</math> | <math>\textbf {(A) } 0\qquad \textbf {(B) }2001^{2002} \qquad \textbf {(C) }2002^{2003} \qquad \textbf {(D) }2003^{2004} \qquad \textbf {(E) }2001^{2002^{2003}}</math> | ||
Revision as of 09:01, 6 September 2021
Problem
The set of all real numbers 
for which
![\[\log_{2004}(\log_{2003}(\log_{2002}(\log_{2001}{x})))\]](http://latex.artofproblemsolving.com/e/f/a/efaf7382f309efe8361302a7c57315c0e92e4adb.png)
is defined is 
. What is the value of 
?
Solution
For all real numbers 
and such that 
note that:
is defined if and only if 
if and only if 
is defined if and only if 
if and only if 
Therefore, we have
from which 
~Azjps (Fundamental Logic)
~MRENTHUSIASM (Reconstruction)
See also
| 2004 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 15 |
Followed by Problem 17 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
