若log2[log12(log2x)]＝log3[log13(log3y)]＝log5[log15(log5z)]=0，则x、y、_数学解答

若log₂[log

(log2x)]＝log3[log

(log3y)]＝log5[log

(log5z)]=0，则x、y、z的大小关系是（　　）
A. z<x<y
B. x<y<z
C. y<z<x
D. z<y<x

人气：479 ℃　时间：2020-05-09 19:30:44

解答

∵log2[log12(log2x)]＝log3[log13(log3y)]＝log5[log15(log5z)]=0，∴log12(log2x) ＝log13(log3y)=log15(log5z)=1，∴log2x＝12，log3y＝13，log5z＝15，∴x＝2，y＝33，z=55，∴z<x<y．故选A．...