document.write( "Question 982914: x= 1+log[base a]bc , y= 1+log[base b]ca , z= 1+log[base c]ab. Then PROVE THAT :
\n" ); document.write( "xy+yz+zx=xyz \n" ); document.write( "

Algebra.Com's Answer #603727 by anand429(138) $\"\"$ $\"About$

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$\"x=+1%2Blog%28a%2Cbc%29\"$
\n" ); document.write( "=> $\"x=+log%28a%2Ca%29%2Blog%28a%2Cbc%29\"$
\n" ); document.write( "=> $\"x=+log%28a%2Cabc%29\"$
\n" ); document.write( "Similarly,
\n" ); document.write( " $\"y=+log%28b%2Cabc%29\"$
\n" ); document.write( "and $\"z=+log%28c%2Cabc%29\"$
\n" ); document.write( "Now,
\n" ); document.write( "

\n" ); document.write( "=> $\"1%2Fx+%2B+1%2Fy+%2B+1%2Fz+=+log%28abc%2Ca%29+%2B+log%28abc%2Cb%29+%2B+log%28abc%2Cc%29\"$
\n" ); document.write( "=> $\"1%2Fx+%2B+1%2Fy+%2B+1%2Fz+=+log%28abc%2Cabc%29\"$
\n" ); document.write( "=> $\"1%2Fx+%2B+1%2Fy+%2B+1%2Fz+=+1\"$
\n" ); document.write( "Multiplying both sides by xyz, we get,
\n" ); document.write( " $\"yz+%2B+xz+%2B+xy+=+xyz\"$ Proved. \n" ); document.write( "

\n" );