1.对任意 y≠ 0
f(1) = f(1^y) = yf(1)
f(1) = 0
2.对任意 实数 x,y
f(x)*f(y) = f(x^f(y)) = f(y^f(x))
x^f(y) = y^f(x)
f(y)*lgx = f(x)*lgy
f(x)/f(y) = lgx/lgy
f(x) = klgx k为常数
a,b,c成等比数列,b*b = ac
f(a)f(c)
= k^2 lga*lgc
≤k^2 [(lga+lgc)/2]^2
= k^2 [lg(ac)/2]^2
= k^2 [lg(b^2) /2 ] ^2
=( klgb)^2
= [f(b)]^2
3.f(1/2)
= klg(1/2)
< 0
(1/2)^k < 1
k > 0
f(x) = klgx,k>0,f(x)在(0,+∞）上是增函数