3n−−√3 = 27,3n3 = 27,\root 3 \of {{3^n}} {\text{ = 27,}} then the value of n is = ?" /> 3n−−√3 = 27,3n3 = 27,\root 3 \of {{3^n}} {\text{ = 27,}} then the value of n is = ?" /> 3n−−√3 = 27,3n3 = 27,\root 3 \of {{3^n}} {\text{ = 27,}} then the value of n is = ?" />

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If $\sqrt[3]{3^{n}} = 27,$ $\root 3 \of {{3^n}} {\text{ = 27,}}$ then the value of n is = ?

Answer:- 1

Explanation:-

Solution:

According to question

\begin{aligned} \sqrt[3]{3^{n}} =  27 \\ \Rightarrow {(3^{n})}^{\frac{1}{3}} = {(3)}^{3} \\ \Rightarrow 3^{\frac{n}{3}} = 3^{3} \\ \Rightarrow \frac{n}{3} = 3 \\ \Rightarrow n = 9 \end{aligned}

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then the value of n is = ?", "text": "If

\sqrt[3]{3^{n}} =  27,

$\root 3 \of {{3^n}} {\text{ = 27,}}$ then the value of n is = ?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

According to question

\begin{aligned} \sqrt[3]{3^{n}} =  27 \\ \Rightarrow {(3^{n})}^{\frac{1}{3}} = {(3)}^{3} \\ \Rightarrow 3^{\frac{n}{3}} = 3^{3} \\ \Rightarrow \frac{n}{3} = 3 \\ \Rightarrow n = 9 \end{aligned}

$\eqalign{ & \root 3 \of {{3^n}} {\text{ = 27}} \cr & \Rightarrow {\left( {{3^n}} \right)^{\frac{1}{3}}} = {\left( 3 \right)^3} \cr & \Rightarrow {3^{\frac{n}{3}}} = {3^3} \cr & \Rightarrow \frac{n}{3} = 3 \cr & \Rightarrow n = 9 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

According to question