If log1000x=−14, then the value of x is = ? If log1000x=−14, then the value of x is = ? \eqalign{ & {\text{If }}{\log _{1000}}x = - \frac{1}{4}{\text{, }} \cr & {\text{then the value of }}x{\text{ is = ? }} \cr} " /> If log1000x=−14, then the value of x is = ? If log1000x=−14, then the value of x is = ? \eqalign{ & {\text{If }}{\log _{1000}}x = - \frac{1}{4}{\text{, }} \cr & {\text{then the value of }}x{\text{ is = ? }} \cr} " /> If log1000x=−14, then the value of x is = ? If log1000x=−14, then the value of x is = ? \eqalign{ & {\text{If }}{\log _{1000}}x = - \frac{1}{4}{\text{, }} \cr & {\text{then the value of }}x{\text{ is = ? }} \cr} " />

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$\begin{aligned} If \log_{1000} x = - \frac{1}{4}, \\ then the value of x is = ? \end{aligned}$ $\eqalign{ & {\text{If }}{\log _{1000}}x = - \frac{1}{4}{\text{, }} \cr & {\text{then the value of }}x{\text{ is = ? }} \cr}$

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} let \log_{1000} x = - \frac{1}{4} \\ \Rightarrow x = {(10000)}^{- \frac{1}{4}} \\ = {(10^{4})}^{- \frac{1}{4}} \\ = 10^{- 1} \\ = \frac{1}{10} \end{aligned}

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", "text": "

\begin{aligned} If \log_{1000} x = - \frac{1}{4}, \\ then the value of x is = ? \end{aligned}

$\eqalign{ & {\text{If }}{\log _{1000}}x = - \frac{1}{4}{\text{, }} \cr & {\text{then the value of }}x{\text{ is = ? }} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} let \log_{1000} x = - \frac{1}{4} \\ \Rightarrow x = {(10000)}^{- \frac{1}{4}} \\ = {(10^{4})}^{- \frac{1}{4}} \\ = 10^{- 1} \\ = \frac{1}{10} \end{aligned}

$\eqalign{ & {\text{let }}{\log _{1000}}{\text{x}} = - \frac{1}{4} \cr & \Rightarrow {\text{ x}} = {\left( {10000} \right)^{ - \frac{1}{4}}} \cr & = {\left( {{{10}^4}} \right)^{ - \frac{1}{4}}} \cr & = {10^{ - 1}} \cr & = \frac{1}{{10}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution: