Difference between revisions of "1998 AHSME Problems/Problem 12"
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| − | + | == 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 18:18, 11 August 2008
Problem
How many different prime numbers are factors of 
if
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 | ||
