X = a^t
=> log(a)x = t
3log(x)a = 3log(a)a/log(a)x= 3/t
log(x)y = log(a)y/log(a)x = log(a)y/t
代入原式有:t + 3/t - log(a)y/t = 3
=> t^2 – 3t +3 = log(a)y
=> y = a(t^2 – 3t +3)
对数中()内的是底
若a=16 代入上式有:
y = 16(t^2 – 3t +3) =16[(t-3/2)^2 + 3/4]
所以Y最小是当t = 3/2时,即163/4=8,所以Y>=8