Question
If $${\log _{10000}}x = - \frac{1}{4}{\text{,}}$$ then the value of x is = ?
Answer: Option A
$$\eqalign{
& {\text{let }}{\log _{10000}}x = - \frac{1}{4} \cr
& \Rightarrow x = {\left( {10000} \right)^{ - \frac{1}{4}}} \cr
& = {\left( {{{10}^4}} \right)^{ - \frac{1}{4}}} \cr
& = {10^{ - 1}} \cr
& = \frac{1}{{10}} \cr} $$
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$$\eqalign{
& {\text{let }}{\log _{10000}}x = - \frac{1}{4} \cr
& \Rightarrow x = {\left( {10000} \right)^{ - \frac{1}{4}}} \cr
& = {\left( {{{10}^4}} \right)^{ - \frac{1}{4}}} \cr
& = {10^{ - 1}} \cr
& = \frac{1}{{10}} \cr} $$
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