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1998 AHSME Problems/Problem 12

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Problem

How many different prime numbers are factors of N 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 N = 7^{5^{3^{2^{11}}}}, which only has 7 as a prime factor \mathbf{(A)}.

See also

1998 AHSME (Problems)
Preceded by
Problem 11
Followed by
Problem 13
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