Difference between revisions of "1998 AHSME Problems/Problem 12"
(1998 AHSME Problems/Problem 12 moved to 1998 AHSME: o_o) |
(solution) |
||
Line 1: | Line 1: | ||
− | + | == Problem == | |
+ | How many different prime numbers are factors of <math>N</math> if | ||
+ | |||
+ | <center><math>\log_2 ( \log_3 ( \log_5 (\log_ 7 N))) = 11?</math></center> | ||
+ | |||
+ | <math> \mathrm{(A) \ }1 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }3 \qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ }7 </math> | ||
+ | |||
+ | == Solution == | ||
+ | Re-writing as exponents, we have <math>\log_3 ( \log_5 (\log_ 7 N)) = 2^{11}</math>, and so forth, such that <math>N = 7^{5^{3^{2^{11}}}}</math>, which only has <math>7</math> as a prime factor <math>\mathbf{(A)}</math>. | ||
+ | |||
+ | == See also == | ||
+ | {{AHSME box|year=1998|num-b=11|num-a=13}} | ||
+ | |||
+ | [[Category:Introductory Algebra Problems]] |
Revision as of 19:18, 11 August 2008
Problem
How many different prime numbers are factors of if
![$\log_2 ( \log_3 ( \log_5 (\log_ 7 N))) = 11?$](http://latex.artofproblemsolving.com/3/e/2/3e299a9c249c24f7ece706fabc28efdbb48b77cd.png)
Solution
Re-writing as exponents, we have , and so forth, such that
, which only has
as a prime factor
.
See also
1998 AHSME (Problems • Answer Key • Resources) | ||
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 | ||
All AHSME Problems and Solutions |