设xyz均为正数,且3的x次方=4的y次方=6的z次方 求x y z之间的关系 比较3x 4y 6z的大小

设3^x=4^y=6^z=k.x=log3(k)=1/logk(3),y=log4(k)=1/logk(4),z=log6(k)=1/logk(6)1,1/x+1/(2y)=logk(3)+logk(4)/2=logk(3)+logk(2)=logk(6)=1/z 所以1/x+1/(2y)=1/z2,3^(1/3)=3^(4/12)=81^(1/12) 4^(1/4)=4^(3/12...