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
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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/z

2,3^(1/3)=3^(4/12)=81^(1/12)

4^(1/4)=4^(3/12)=64^(1/12)

6^(1/6)=6^(2/12)=36^(1/12)

3^(1/3)>4^(1/4)>6^(1/6),logk(3)/3>logk(4)/4>logk(6)/6

3/logk(/3)

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