已知函数f(x)=log2(x+m),且f(0),f(2),f(6)成等差数列.

问题描述:

已知函数f(x)=log2(x+m),且f(0),f(2),f(6)成等差数列.
求实数m的值.2,若a,b,c是两个不等的正数,且a,b,c成等比数列,试判断f(a)+f(c)与2f(b)的大小关系,并证明结论.

f(0)=log2 m
f(2)=log2 (m+2)
f(6)=log2 (m+6)
2f(2)=f(0)+f(6)
2log2 (m+2)=log2 (m+6)+log2 m
log2 (m+2)^2=log2 (m^2+6m)
m^2+4m+4=m^2+6m
m=2