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The value of x satisfying the equation [3(1 - 1/2 + 1/4 .....Infinity)]^log x base 10 = [20(1 - 1/4 + 1/16 .....Infinity)]^log 10base x

The value of x satisfying the equation [3(1 - 1/2 + 1/4 .....Infinity)]^log x base 10 = [20(1 - 1/4 + 1/16 .....Infinity)]^log 10base x

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1 Answers

Aditya Gupta
2081 Points
4 years ago
note that log 10base x= 1/log x base 10
so let log x base 10=y
also 3(1 - 1/2 + 1/4 .....Infinity)= 3/(3/2)= 2
and 20(1 - 1/4 + 1/16 .....Infinity)= 20*4/5= 16
so 2^y=16^(1/y)
or 2^y=2^(4/y)
or y=4/y
y= +-2= log x base 10
so x= 10^2 and 10^-2
so x= 100 or 1/100

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