SOLUTION: x= 1+log[base a]bc , y= 1+log[base b]ca , z= 1+log[base c]ab. Then PROVE THAT : xy+yz+zx=xyz

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: x= 1+log[base a]bc , y= 1+log[base b]ca , z= 1+log[base c]ab. Then PROVE THAT : xy+yz+zx=xyz      Log On


   

Question 982914: x= 1+log[base a]bc , y= 1+log[base b]ca , z= 1+log[base c]ab. Then PROVE THAT :
xy+yz+zx=xyz
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
x=+1%2Blog%28a%2Cbc%29
=> x=+log%28a%2Ca%29%2Blog%28a%2Cbc%29
=> x=+log%28a%2Cabc%29
Similarly,
y=+log%28b%2Cabc%29
and z=+log%28c%2Cabc%29
Now,

=> 1%2Fx+%2B+1%2Fy+%2B+1%2Fz+=+log%28abc%2Ca%29+%2B+log%28abc%2Cb%29+%2B+log%28abc%2Cc%29
=> 1%2Fx+%2B+1%2Fy+%2B+1%2Fz+=+log%28abc%2Cabc%29
=> 1%2Fx+%2B+1%2Fy+%2B+1%2Fz+=+1
Multiplying both sides by xyz, we get,
yz+%2B+xz+%2B+xy+=+xyz Proved.