函数y=log2(x)+logx(2x)的值域是

问题描述:

函数y=log2(x)+logx(2x)的值域是

log2(x)+log2(2x)/log2(x)=log2(x)+/log2(x)=log2(x)+1/log2(x)+1
当log2(x)小于等于-2〈log2(x)*1/log2(x)>+1= -1
当log2(x)>0时 用均值定理 大于等于2〈log2(x)*1/log2(x)>+1=3
故值域为(-∞,-1]∪[3,+∞)

y=log2(x)+logx(2x)=log2(x)+logx(2)+logx(x)=log2(x)+logx(2)+1
log2(x)与logx(2)互为倒数,故值域为(-∞,-1]∪[3,+∞)