f(x)=Log2(x+m)
f(0)=Log2(m)
f(2)=Log2(2+m)
f(6)=Log2(6+m)
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
6m+m^2=4+4m+m^2
2m=4
m=2
f(x)=Log2(x+2)
(1)。
f(30)=Log2(30+2)=Log2(32)=5
(2)。
三正数a,b,c等比:b^2=ac
f(a)+f(c)=
Log2(a+2)+Log2(c+2)=
Log2[(a+2)*(c+2)]=
Log2[(ac)+2(a+c)+4]=
Log2[b^2+2(a+c)+4](a,b,c0且互不相等)
Log2[b^2+4√(a*c)+4]=
Log2[b^2+4b+4]=
Log2(b+2)^2=
2f(b)
∴f(a)+f(c)2f(b)
0