Преобразуем сначало так:
( (log(5;7√5)-log(5;7))^2 + log(5;7)*( log(5;7)-log(5;7√5) ) )/(log(5;7√5)-log(5;49) )= ((log(5;√5))^2-log(5;7)*log(5;√5))/log(5;√5/7)=(1/4-1/2*log(5;7))/log(5;√5/7)=1/4*(1-2log(5;7)/log(5;√5/7)=1/4*(log(5;5)-log(5;49))/log(5;√5/7)=1/4*log(5;5/49)/log(5;√5/7)=1/2*log(5;√5/7)/log(5;√5/7)=1/2 (Тк (√5/7)^2=5/49)
Ответ: 1/2