设f(x)=log2^x-logx^4(0

问题描述:

设f(x)=log2^x-logx^4(0
求详解:分子有理化!

(1)
f(x)=log2X-logx4=log2X-log2(4)/log2X
=log2X-2/log2X
f(2的an次方)=2n
即log2(2的an次方)-2/log2(2的an次方)=an-2/an=2n
an^2-2n·an-2=0 (1)
此时2的an次方应该满足函数的定义域,即0