1題高職數學(指數)~~~
回答 (3)
2011-10-23 5:15 pm
2011-10-23 7:38 pm
大大們的回答難分軒輊,交給網友們吧^^
2011-10-23 9:34 am
a^xb^y=b^xc^y=c^xa^y=abc≠1，x+y=?
Sol
abc<>1
log(abc)<>0
a^xb^y=b^xc^y=c^xa^y=abc
log(a^xb^y)=log(b^xc^y)=log(c^xa^y)=log(abc)
log(a^x)+log(b^y)=log(b^x)+log(c^y)=log(c^x)+log(a^y)=log(abc)
xloga+ylogb=xlogb+ylogc=xlogc+yloga=log(abc)
(xloga+ylogb)+(xlogb+ylogc)+(xlogc+yloga)=3log(abc)
loga(x+y)+logb(y+x)+logx(y+x)=3log(abc)
[(x+y)-3]log(abc)=0
Log(abc)<>0
x+y－3=0
x+y=3
Sol
abc<>1
log(abc)<>0
a^xb^y=b^xc^y=c^xa^y=abc
log(a^xb^y)=log(b^xc^y)=log(c^xa^y)=log(abc)
log(a^x)+log(b^y)=log(b^x)+log(c^y)=log(c^x)+log(a^y)=log(abc)
xloga+ylogb=xlogb+ylogc=xlogc+yloga=log(abc)
(xloga+ylogb)+(xlogb+ylogc)+(xlogc+yloga)=3log(abc)
loga(x+y)+logb(y+x)+logx(y+x)=3log(abc)
[(x+y)-3]log(abc)=0
Log(abc)<>0
x+y－3=0
x+y=3
收錄日期: 2021-05-02 10:44:11
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111023000010KK00483