log2log3log4x=log3log4log2y=log4log2log3z,求x+y+z等于多少log2log3log4x中,2是最外层对数的底数,真数是log3那部分,log4又是log3的真数．x是log4的真数．以后两个式子是同理．

Question

log2log3log4 x =log3log4log2 y =log4log2log3 z ,求x+y+z等于多少
log2log3log4 x中,2是最外层对数的底数,真数是log3那部分,log4又是log3的真数．x是log4的真数．以后两个式子是同理．

Answer 1

条件不足啊.
比如x=4^3,y=2^4,z=3^2,则
log2log3log4 x =log3log4log2 y =log4log2log3 z=0成立
又比如x=4^9,y=2^64,z=3^16,则
log2log3log4 x =log3log4log2 y =log4log2log3 z=1成立