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2005 AMC 12B Problems/Problem 17

Revision as of 17:18, 21 February 2010 by Fuzzy growl (talk | contribs) (→‎Problem)

Problem

How many distinct four-tuples $(a,b,c,d)$ of rational numbers are there with

\[a\cdot\log_{10}2+b\cdot\log_{10}3+c\cdot\log_{10}5+d\cdot\log_{10}7=2005?\]

$\mathrm{(A)}\ 0 \qquad \mathrm{(B)}\ 1 \qquad \mathrm{(C)}\ 17 \qquad \mathrm{(D)}\ 2004 \qquad \mathrm{(E)}\ \text{infinitely many}$

Solution

See also

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