已知f(x)={2^x,(x≥4);f(x+1)(x
问题描述：
已知f(x)={2^x,(x≥4);f(x+1)(x
答
解log2(3)＜log2（16）=4
故f(log2(3))=f(log2(3)+1)=f(log2(3)+log2（2）)=f(log2(6))
而log2(6)＜log2（16）=4
f(log2(3))=f(log2(6))=f(log2(6)+1)=f(log2(6)+log2（2）)=f(log2(12))
而log2(12)＜log2（16）=4
故f(log2(3))=f(log2(6))=f(log2(12))=f(log2(12)+1)=f(log2(24))
而log2(24)＞log2（16）=4
故f(log2(3))=f(log2(6))=f(log2(12))=f(log2(24))
=2^(log2(24))
=24.
答
∵ log2(3)∈(1,2)∴ f(log2(3))=f(log2(3)+1)=f(log2(6))∵ log2(6)∈(2,3)=f(log2(6)+1)=f(log2(12))∵ log2(12)∈(3,4)=f(log2(12)+1)=f(log2(24)∵ log2(24)∈(4,5)=2^(log2(24))=24