Question

已知log[ log( logx)] = log[ log( logy)] = log[ log( logz)] = 0，试比较x、y、z的大小．

Answer 1

由log[ log( logx)] = 0得，log( logx)= 1，logx =，即x = 2；

由log[ log( logy)] = 0得，log( logy) = 1，logy =，即y =3；由log[ log( logz)] = 0得，log( logz) = 1，logz =，即z = 5．

∵y =3= 3= 9，∴x = 2= 2= 8，∴y＞x，又∵x = 2= 2= 32，z = 5= 5= 25，∴x＞z．

故y＞x＞z．