AMC 12B 2005 Problem 17

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

a \log _{10} 2+b \log _{10} 3+c \log _{10} 5+d \log _{10} 7=2005 ?

Answer Choices
A. 0
B. 1
C. 17
D. 2004
E. infinitely many