AHSME 1995 Problem 24

There exist positive integers $A,B$ and $C$, with no common factor greater than $1$, such that $$A \log_{200} 5 + B \log_{200} 2 = C.$$ What is $A + B + C$?

$\mathrm{(A) \ 6 } \mathrm{(B) \ 7 } \mathrm{(C) \ 8 } \mathrm{(D) \ 9 } \mathrm{(E) \ 10 }$