y=(2+log3x)^2+2+log3(x^2)
=(log3x)^2+4log3x+4+2log3x+2
=(log3x)^2+6log3x+6
=(3+log3x)^2-3
x∈[1,3]
log3x∈[0,1]
3+log3x∈[3,4]
(3+log3x)^2∈[9,16]
y=(3+log3x)^2-3∈[6,13]
y=(2+log3x)^2+2+log3(x^2)
=(log3x)^2+4log3x+4+2log3x+2
=(log3x)^2+6log3x+6
=(3+log3x)^2-3
x∈[1,3]
log3x∈[0,1]
3+log3x∈[3,4]
(3+log3x)^2∈[9,16]
y=(3+log3x)^2-3∈[6,13]