AoPSWiki
Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
Personal tools

1998 AHSME Problems/Problem 12

From AoPSWiki

Problem

How many different prime numbers are factors of if

\log_2 ( \log_3 ( \log_5 (\log_ 7 N))) = 11?

\mathrm{(A) \ }1 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }3 \qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ }7

Solution

Re-writing as exponents, we have \log_3 ( \log_5 (\log_ 7 N)) = 2^{11}, and so forth, such that , which only has as a prime factor .

See also

1998 AHSME (Problems)
Preceded by
Problem 11
Followed by
Problem 13
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 26 27 28 29 30
Support local problem solving programs by contributing to the Art of Problem Solving Foundation.
Click here for more information about the Foundation.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • FoundationPrivacyContact Us