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Magical Mathematics[Interesting Approach]

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

suresh parasa

7 Years agoGrade

1 Answer

Aditya Gupta

7 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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