Difference between revisions of "2005 AMC 12B Problems/Problem 17"
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== Problem == | == Problem == | ||
| + | |||
| + | How many distinct four-tuples <math>(a,b,c,d)</math> of rational numbers are there with | ||
| + | |||
| + | <cmath>a\cdot\log_{10}2+b\cdot\log_{10}3+c\cdot\log_{10}5+d\cdot\log_{10}7=2005?</cmath> | ||
| + | |||
| + | <math> | ||
| + | \mathrm{(A)}\ 0 \qquad | ||
| + | \mathrm{(B)}\ 1 \qquad | ||
| + | \mathrm{(C)}\ 17 \qquad | ||
| + | \mathrm{(D)}\ 2004 \qquad | ||
| + | \mathrm{(E)}\ \text{infinitely many} | ||
| + | </math> | ||
== Solution == | == Solution == | ||
Revision as of 18:18, 21 February 2010
Problem
How many distinct four-tuples 
of rational numbers are there with
![\[a\cdot\log_{10}2+b\cdot\log_{10}3+c\cdot\log_{10}5+d\cdot\log_{10}7=2005?\]](http://latex.artofproblemsolving.com/9/1/5/9153c41adf40f93e619e0362b706aa5160874e9c.png)
