document.write( "Question 971266: If a,b,c………… be in G.P,then show that loga x,logb x,logc x, ……… are in H.P \n" ); document.write( "

Algebra.Com's Answer #594095 by anand429(138) $\"\"$ $\"About$

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Given, a,b,c are in GP,
\n" ); document.write( "So, let common factor be k such that b=ak and c=ak^2.
\n" ); document.write( "Now for checking the H.P. of given terms,
\n" ); document.write( " $\"1%2Flog%28a%2Cx%29-1%2Flog%28b%2Cx%29\"$
\n" ); document.write( "= $\"log%28x%2Ca%29-log%28x%2Cb%29\"$
\n" ); document.write( "= $\"log%28x%2C%28a%2Fb%29%29\"$
\n" ); document.write( "= $\"log%28x%2C%28a%2F%28a%2Ak%29%29%29\"$
\n" ); document.write( "= $\"log%28x%2C%281%2Fk%29%29\"$ -(i)
\n" ); document.write( "Again,
\n" ); document.write( " $\"1%2Flog%28b%2Cx%29-1%2Flog%28c%2Cx%29\"$
\n" ); document.write( "= $\"log%28x%2Cb%29-log%28x%2Cc%29\"$
\n" ); document.write( "= $\"log%28x%2C%28b%2Fc%29%29\"$
\n" ); document.write( "= $\"log%28x%2C%28%28a%2Ak%29%2F%28a%2Ak%5E2%29%29%29\"$
\n" ); document.write( "= $\"log%28x%2C%281%2Fk%29%29\"$ -(ii)
\n" ); document.write( "So, from (i) and (ii),
\n" ); document.write( " $\"1%2Flog%28a%2Cx%29-1%2Flog%28b%2Cx%29+=+1%2Flog%28b%2Cx%29-1%2Flog%28c%2Cx%29\"$
\n" ); document.write( "Hence, $\"log%28a%2Cx%29\"$ , $\"log%28b%2Cx%29\"$ and $\"log%28c%2Cx%29\"$ are in H.P. \n" ); document.write( "

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