31 x次方=27 279 y次方=81 求3/x-4/y?
回答 (4)
2017-01-17 7:48 am
Sol
31^x=27
xlog31=log27
x=log27/log31
1/x=log31/log27
279^y=81
ylog279=log81
y(log9+log31)=log81
y=log81/(log9+log31)
1/y=(log9+log31)/log81
3/x－4/y
=3log31/log27－4(log9+log31)/log81
=log31/log3－(log9+log31)/log3
=－log9/log3
=－2
31^x=27
xlog31=log27
x=log27/log31
1/x=log31/log27
279^y=81
ylog279=log81
y(log9+log31)=log81
y=log81/(log9+log31)
1/y=(log9+log31)/log81
3/x－4/y
=3log31/log27－4(log9+log31)/log81
=log31/log3－(log9+log31)/log3
=－log9/log3
=－2
2017-01-20 4:21 pm
分別對31^x=27以及279^y=81取3為底的log，移項整理後
log(31)=3/x，log(279)=4/y，
故3/x-4/y= log(31)- log(279)= log(31/279)= -2
log(31)=3/x，log(279)=4/y，
故3/x-4/y= log(31)- log(279)= log(31/279)= -2
參考: 醬料
2017-01-17 12:22 am
-2
收錄日期: 2021-04-30 22:03:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170116155406AAKMCFq