If log2aa=x,log3a2a=y and log4a3a=z then xyz-2yz is equal to

Asked by Anil | 3rd May, 2017, 06:53: PM

Expert Answer:

begin mathsize 16px style space log subscript 2 straight a end subscript straight a equals straight x comma log subscript 3 straight a end subscript 2 straight a equals straight y space and space log subscript 4 straight a end subscript 3 straight a equals straight z space
xyz minus 2 yz equals log subscript 2 straight a end subscript straight a cross times log subscript 3 straight a end subscript 2 straight a cross times log subscript 4 straight a end subscript 3 straight a minus 2 log subscript 3 straight a end subscript 2 straight a cross times space log subscript 4 straight a end subscript 3 straight a
space space space space space space space space space space space space space space space space space space equals fraction numerator loga over denominator log 2 straight a end fraction cross times fraction numerator log 2 straight a over denominator log 3 straight a end fraction cross times fraction numerator log 3 straight a over denominator log 4 straight a end fraction minus 2 cross times fraction numerator log 2 straight a over denominator log 3 straight a end fraction cross times fraction numerator log 3 straight a over denominator log 4 straight a end fraction
space space space space space space space space space space space space space space space space space space equals fraction numerator loga over denominator log 4 straight a end fraction minus 2 cross times fraction numerator log 2 straight a over denominator log 4 straight a end fraction
space space space space space space space space space space space space space space space space space space space equals log subscript 4 straight a end subscript straight a minus log subscript 4 straight a end subscript 4 straight a squared
space space space space space space space space space space space space space space space space space space space space equals log subscript 4 straight a end subscript fraction numerator 1 over denominator 4 straight a end fraction equals negative 1

end style

Answered by Sneha shidid | 4th May, 2017, 09:59: AM