y=[log(1/4)x]^2-log(1/4)x^2+5
=[log(1/4)x]^2-2log(1/4)x+5
=[log(1/4)x-1]^2+4
∵x∈[2,4],log(1/4)x-1好像答案不对吧是错了，抱歉y=[log(1/4)x]^2-log(1/4)x^2+5 =[log(1/4)x]^2-2log(1/4)x+5 =[log(1/4)x-1]^2+4∵x∈[2,4],log(1/4)x<0∴在区间[2,4]单调递增当x=2时,y=[log(1/4)2-1]^2+4=25/4当x=4时,y=[log(1/4)4-1]^2+4=8y∈[25/4,8]