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  • If a^x =b^y=c^z and x , y ,z are in GP prove that log a ( base b) = log b ( base c)

If a^x =b^y=c^z and x , y ,z are in GP prove that log a ( base b) = log b ( base c)

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Solution:             a^x=b^y=c^z

              Taking  logarithm , we get 

                                 xlog a= ylog b=zlog c

             Rightarrow                fracyx=fraclog alog b=log_ba         ...........(1)

             and             fraczy=fraclog blog c=log_cb          ...........(2)

             But  given     x , y , z   are in GP .

              herefore              fracyx=fraczyRightarrow log_ba=log_cb     From  (1) and (2)                    

Posted by

Deependra Verma

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