f(x)满足f(x^m)=mf(x)和f(a)=1(a>1)证f(xy)=f(x)+f(y)单调递增

f(x)满足f(x^m)=mf(x)和f(a)=1(a>1)证f(xy)=f(x)+f(y)单调递增
f(x)满足f(x^m)=mf(x)和f(a)=1(a>1)
证f(xy)=f(x)+f(y)
单调递增

f(x)满足f(x^m)=mf(x)和f(a)=1(a>1)证f(xy)=f(x)+f(y)单调递增
令y=x^(m-1),则左边等于f(xy)=f(x^m)=mf(x),右边等于f(x)+f(y)=f(x)+f(x^(m-1))=f(x)+(m-1)f(x)=mf(x),左边等于右边,得证!