已知f(X)=1+logx3,g(X)=2log3(x>0,x不等于1),比较fx与gx大小

问题描述:

已知f(X)=1+logx3,g(X)=2log3(x>0,x不等于1),比较fx与gx大小

y=1+log(x)3-2log(x)2
=log(x)x+log(x)3-log(x)4
=log(x)(3x/4)
当1>x>0时,3x/40,即1+log(x)3>2logx2
当4/3>x>1时,3x/40,即1+log(x)3>2logx2