设函数f（x）满足f(x)＝1+f(12)•log2x，则f（2）=．

Question

设函数f（x）满足f(x)＝1+f((1)/(2))•log2x，则f（2）=______．

Answer 1

因为f(x)＝1+f((1)/(2))•log2x，
所以f((1)/(2))＝1+f((1)/(2))•log2(1)/(2)．
f((1)/(2))＝(1)/(2)，
∴f(x)＝1+(1)/(2)•log2x．
∴f(2)＝1+(1)/(2)•log22=(3)/(2)．
故答案为：(3)/(2)．