求函數y=log2(x)+log x(2x)的值域

求函數y=log2(x)+log x(2x)的值域

答:
y=log2(x)+logx(2x)
定義域滿足:x>0,x≠1
根據換底公式有:
y=log2(x)+logx(2x)
=log2(x)+log2(2x)/log2(x)
=log2(x)+[1+log2(x)]/log2(x)
=log2(x)+1/log2(x)+1設m=log2(x)
=m+1/m+1
1)當0