Question

If log16 x + (log16 x)^2 + (log16 x)^3 +........=1÷3 then x is​

Answer 1

Answer:

x = 2

Step-by-step explanation:

For

$log_{16}(x) < 0 \\ it \: \: is \: \: a\: \: infinite \: \: gp$

Sum of its infinite terms

$s = \frac{a}{1 - r} = \frac{ log_{16}(x) }{1 - log_{16}(x) } = \frac{1}{3} \: (given) \\ 3 log_{16}(x) = 1 - log_{16}(x) \\ 4 log_{16}(x) = 1 \\ log_{16}(x) = \frac{1}{4} \\ x = {16}^{ \frac{1}{4} } = 2$