document.write( "Question 997978: if logarithm a + logarithm b + logarithm c +.......,is an arithmetic progression, show that a+b+c +.........is a geometric progression \r
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Algebra.Com's Answer #616782 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "Since we are given that\r\n" ); document.write( "\r\n" ); document.write( "log(a) + log(b) + log(c) + ... is an arithmetic progression,\r\n" ); document.write( "\r\n" ); document.write( "then log(b)-log(a) = log(c)-log(b) = ... = the common difference\r\n" ); document.write( "\r\n" ); document.write( "Therefore by a principle of logs, log(b/a) = log(c/d) = ... \r\n" ); document.write( "\r\n" ); document.write( "Therefore b/a = c/d = ... = common ratio of a,b,c,...\r\n" ); document.write( "\r\n" ); document.write( "Therefor a,b,c,... is a geometric progression.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " |