设f(x)={f(x+2) (x<4),(1/2)的x次方 (x≧4)}求f(1+㏒以2为底以3为真数的函数)的值
问题描述:
设f(x)={f(x+2) (x<4),(1/2)的x次方 (x≧4)}求f(1+㏒以2为底以3为真数的函数)的值
答
首先2<1+log(2)(3)<4
那么4<3+log(2)(3)
f(1+log(2)(3))=f(3+log(2)(3))=1/2^(3+log(2)(3))=(1/2)^3×(1/2)^(log(2)(3))
=1/8×(1/3)=1/24注意换算,(1/2)^(log(2)(3))
设2^m=3
log(2)(3)= m
(1/2)^m=1/(2^m)=1/3