设log3(4)*log4(m)=log4(16),求m设log3(4)*log4(m)=log4(16),求m

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 04:58:33
设log3(4)*log4(m)=log4(16),求m设log3(4)*log4(m)=log4(16),求m

设log3(4)*log4(m)=log4(16),求m设log3(4)*log4(m)=log4(16),求m
设log3(4)*log4(m)=log4(16),求m
设log3(4)*log4(m)=log4(16),求m

设log3(4)*log4(m)=log4(16),求m设log3(4)*log4(m)=log4(16),求m
log3(4)×log4(m)=log4(16)
(lg4/lg3)×(lgm/lg4)=2
lgm/lg3=2
log3(m)=2=log3(9)
m=9
===========
非常好用的对数换底公式:log(a)b=lgb/lga
===========
证明:设log(a)b=t
则a^t=b,两边取以10为底的对数
lga^t=lgb
tlga=lgb
所以t=lgb/lga
所以log(a)b=lgb/lga

因为log4(16)=2
所以log3(4)*log4(m)=2
所以3^(log3(4)*log4(m))=3^2=9
即4^log4(m)=9
所以m=9

log3(4)=lg4/lg3...a
log4(m)=lgm/lg4...b
ab=2=lgm/lg3=log3(m)
m=3^2=9