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Examveda

If $${\log _{1000}}x = - \frac{1}{4}{\text{,}}$$    then the value of x is = ?

A. $$\frac{1}{{10}}$$

B. $$\frac{1}{{100}}$$

C. $$\frac{1}{{1000}}$$

D. $$\frac{1}{{10000}}$$

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {\text{let }}{\log _{1000}}{\text{x}} = - \frac{1}{4} \cr & \Rightarrow {\text{ x}} = {\left( {10000} \right)^{ - \frac{1}{4}}} \cr & = {\left( {{{10}^4}} \right)^{ - \frac{1}{4}}} \cr & = {10^{ - 1}} \cr & = \frac{1}{{10}} \cr} $$

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