设x,y,z∈正实数,且3的x次方=4的y次方=6的z次方,比较3x,4y,6z的大小

3^x=4^y=6^z=t＞0x=log3 ty=log4 tz=log6 t3x=3log3 t=log3^(1/3) t 4y=4log4 t=log4^(1/4) t 6z=6log6 t=log6^(1/6) t 3^1/3＞4^1/4＞6^1/6都＞1∴log6^(1/6) t＞log4^(1/4) t＞ log3^(1/3) t6z＞4y＞3x