SOLUTION: If x = 1+ log a bc, y=1+log b ca and z=1+log c ab, prove that xyz = xy+yz+zx.

SOLUTION: If x = 1+ log a bc, y=1+log b ca and z=1+log c ab, prove that xyz = xy+yz+zx.

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Question 67011: If x = 1+ log a bc, y=1+log b ca and z=1+log c ab, prove that xyz = xy+yz+zx.
Answer by tanimachatterjee(60) (Show Source): You can put this solution on YOUR website!
x = 1+ log a bc =loga a+ loga bc
= loga abc
therefore 1/x=logabc a
similarly y = log b abc
z= log c abc
(xy +yz+ zx)/xyz
= 1/z + 1/x +1/y
= logabc c +logabc a +logabc b
= log abc abc
=1
(xy +yz+ zx)/xyz = 1
therefore xy + yz +zx =xyz

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