log{5}(45)^1/2+log{5}(5/3)=(1/2)*log{5}(5*3^2)+log{5}(5)-log{5}(3)
=(1/2)*log{5}(5)+(2/2)*log{5}(3)+log{5}(5)-log{5}(3)=(1/2)+log{5}(3)+1-log{5}(3)=(1/2)+1=3/2