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If 3¹⁰ ÷ 27² = 9² × 3ⁿ then the value of n is = ?

110
212
315
430

Answer:- 1

Explanation:-

Solution:

\begin{aligned} 3^{10} \times 2 7^{2} = 9^{2} \times 3^{n} \\ \Rightarrow 3^{10} \times {(3^{3})}^{2} = {(3^{2})}^{2} \times 3^{n} \\ \Rightarrow 3^{10 + 6} = 3^{4 + n} \\ \Rightarrow 10 + 6 = 4 + n \\ \Rightarrow n = 12 \end{aligned}

$\eqalign{ & {{\text{3}}^{10}} \times {\text{2}}{{\text{7}}^2}{\text{ = }}{{\text{9}}^2} \times {{\text{3}}^n} \cr & \Rightarrow {{\text{3}}^{10}} \times {\left( {{3^3}} \right)^2}{\text{ = }}{\left( {{3^2}} \right)^2} \times {{\text{3}}^n} \cr & \Rightarrow {{\text{3}}^{10 + 6}}{\text{ = }}{{\text{3}}^{4 + n}} \cr & \Rightarrow 10 + 6 = 4 + n \cr & \Rightarrow n = 12 \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} 3^{10} \times 2 7^{2} = 9^{2} \times 3^{n} \\ \Rightarrow 3^{10} \times {(3^{3})}^{2} = {(3^{2})}^{2} \times 3^{n} \\ \Rightarrow 3^{10 + 6} = 3^{4 + n} \\ \Rightarrow 10 + 6 = 4 + n \\ \Rightarrow n = 12 \end{aligned}

$\eqalign{ & {{\text{3}}^{10}} \times {\text{2}}{{\text{7}}^2}{\text{ = }}{{\text{9}}^2} \times {{\text{3}}^n} \cr & \Rightarrow {{\text{3}}^{10}} \times {\left( {{3^3}} \right)^2}{\text{ = }}{\left( {{3^2}} \right)^2} \times {{\text{3}}^n} \cr & \Rightarrow {{\text{3}}^{10 + 6}}{\text{ = }}{{\text{3}}^{4 + n}} \cr & \Rightarrow 10 + 6 = 4 + n \cr & \Rightarrow n = 12 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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