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 10:01, 6 September 2021
Problem
The set of all real numbers for which
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
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 |