Question

求函数y=㏒2 x/4*㏒4 x/2(2≤x≤4)的值域?（*表示乘以,2,4为底数,x/4,x/2为真数）

Answer 1

㏒2 x/4=log2 x-log2 4=log2 x-2;

㏒4 x/2=1/2(log2 x-log2 2)=1/2(log2 x-1);

设log2 x=t;

㏒2 x/4*㏒4 x/2=(log2 x-2)(1/2(log2 x-1))=1/2(t-2)(t-1)(1≤x≤2)

值域为[0 1];