The value of (0.2)^ log (1/4 +1/8 +1/16 +....) , where base square root 5

Answers (1)

Solution:       We  have ,

                        (0.2)^log_sqrt5(frac14+frac18+frac116+..........infty )

            Rightarrow        frac14+frac18+frac116+.........+infty =fracfrac141-frac12=frac12=2^-1

            	herefore                (0.2)^log_sqrt5(frac14+frac18+frac116+..........infty )=(frac15)^log_sqrt52^-1  

             Rightarrow                                                                    =(5^-1)^frac-1frac12log_52

             Rightarrow                                                                    =5^2log_52=2^2=4.         

   

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