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 defined is <math>\{x|x > c\}</math>. What is the value of <math>c</math>? |
<math>\text {(A)} 0\qquad \text {(B)}2001^{2002} \qquad \text {(C)}2002^{2003} \qquad \text {(D)}2003^{2004} \qquad \text {(E)}2001^{2002^{2003}}</math> | <math>\text {(A)} 0\qquad \text {(B)}2001^{2002} \qquad \text {(C)}2002^{2003} \qquad \text {(D)}2003^{2004} \qquad \text {(E)}2001^{2002^{2003}}</math> | ||
Revision as of 00:02, 11 February 2008
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
We know that the domain of 
, where 
is a constant, is 
. So 
. By the definition of logarithms, we then have 
. Then 
and 
.
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 | |
