SOLUTION: If x/y +y/x =3, prove that log(x-y)=1/3(log x + log y)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If x/y +y/x =3, prove that log(x-y)=1/3(log x + log y)      Log On


   

Question 1176050: If x/y +y/x =3, prove that log(x-y)=1/3(log x + log y)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Nice problem... but you typed the equation we were supposed to prove incorrectly.

x%2Fy%2By%2Fx=3

%28x%5E2%2By%5E2%29%2F%28xy%29+=+3

x%5E2%2By%5E2+=+3xy

x%5E2-2xy%2By%5E2+=+xy <-- I did that because I know, because of what we are trying to prove, that I somehow need to get from x%5E2%2By%5E2 to x-y

%28x-y%29%5E2+=+xy

log%28%28%28x-y%29%5E2%29%29+=+log%28%28xy%29%29

2%2Alog%28%28x-y%29%29+=+log%28%28x%29%29%2Blog%28%28y%29%29

log%28%28x-y%29%29+=+%281%2F2%29%28log%28%28x%29%29%2Blog%28%28y%29%29%29

The factor is 1/2, not 1/3....