if x=1+log subscript a b c space comma space y equals 1 plus log subscript b c a space comma space z equals 1 plus log subscript c a b space comma space t h e n space p r o v e space t h a t space x y z equals x y plus y z plus z x

Asked by araima2001 | 26th Sep, 2016, 06:07: PM

Expert Answer:

straight x space equals space 1 space plus space log subscript straight a bc space equals space log subscript straight a straight a plus space log subscript straight a bc space equals space space log subscript straight a abc
1 over straight x equals fraction numerator 1 over denominator space space log subscript straight a abc end fraction space equals space space space log subscript abc straight a

straight y space equals space 1 space plus space log subscript straight b ca space equals space log subscript straight b straight b plus space log subscript straight b ca space equals space space log subscript straight b abc
1 over straight y equals fraction numerator 1 over denominator space space space log subscript straight b abc end fraction space equals space space space log subscript abc straight b

straight z space equals space 1 space plus space log subscript straight c ab space equals space log subscript straight c straight c plus space log subscript straight c ab space equals space space log subscript straight c abc
1 over straight z equals fraction numerator 1 over denominator space log subscript straight c abc end fraction space equals space space space log subscript abc straight c

1 over straight x plus 1 over straight y plus 1 over straight z equals space log subscript abc straight a plus space log subscript abc straight b plus space log subscript abc straight c
fraction numerator xy plus yz plus zx over denominator xyz end fraction equals log subscript abc abc

fraction numerator xy plus yz plus zx over denominator xyz end fraction equals 1
xy space plus space yz space plus space zx space equals space xyz

Answered by Vijaykumar Wani | 27th Sep, 2016, 10:10: AM

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