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

题目

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

答案

f(0),f(2),f(6)成等差数列
f(0)+f(6)=2f(2)
log2(m)+log2(6+m)=2log2(2+m)
log2(m(6+m))=log2(2+m)^2
m(6+m)=(2+m)^2
m^2+6m=m^2+4m+4
2m=4
m=2