Math, asked by saipriyapatra, 5 months ago

Time: the
+ - b] J1
JU
math., class - VIII
-2
3
27
L. 97
90x32(3*)2
127 find a
?​

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Answers

Answered by EthicalElite
70

 \huge {\mathtt{Given:-}}

 \sf {9}^{x} \times {3}^{2} \times ( {3}^{ \frac{x}{ - 2} } )^{ - 2} = \frac{1}{27}

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 \huge {\mathtt{To \: Find:-}}

 \sf value \: of \: x

⠀⠀ ⠀

 \huge {\mathtt{Let's \: Do:-}}

 \sf {9}^{x} \times {3}^{2} \times ( {3}^{ \frac{x}{ - 2} } )^{ - 2} = \frac{1}{27}

 \sf {(3}^{2} )^{x} \times {3}^{2} \times ( {3}^{ \frac{x}{ - 2}}) ^{ - 2} = \frac{1}{ {3}^{3} }

 \sf {3}^{2 × x} \times {3}^{2} \times {3}^{ \frac{x}{\cancel{ - 2}} × \cancel{- 2}}   =  {3}^{ - 3}

 \sf {3}^{2x} \times {3}^{2} \times  {3}^{x} = {3}^{ - 3}

 \sf {3}^{ 2x } \times {3}^{2} \times {3}^{x} = {3}^{ - 3}

 \sf {3}^{2x + 2 + x} = {3}^{ - 3}

 \sf {3}^{3x + 2} = {3}^{ - 3}

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Now, the bases are same, so the powers will be equal :-

 \sf \implies 3x + 2 = - 3

 \sf \implies 3x = - 3 - 2

 \sf \implies 3x = - 5

 \sf \implies x = - \frac{5}{3}

 \boxed{\sf x = - \frac{5}{3}}

⠀⠀ ⠀

 \sf \therefore \: value \: of \: x = - \frac{5}{3}

Answered by Anonymous
13

\huge\tt{Answer:-}

 \sf {9}^{x} \times {3}^{2} \times ( {3}^{ \frac{x}{ - 2} } )^{ - 2} = \frac{1}{27}

 \sf {(3}^{2} )^{x} \times {3}^{2} \times {3}^{ \frac{ - 2x}{ - 2} } = \frac{1}{ {3}^{3} }

 \sf {3}^{2x} \times {3}^{2} \times {3}^{x} = {3}^{ - 3}

 \sf {3}^{ 2x } \times {3}^{2} \times {3}^{x} = {3}^{ - 3}

 \sf {3}^{2x + 2 + x} = {3}^{ - 3}

 \sf {3}^{3x + 2} = {3}^{ - 3}

Now, the bases are same, so the powers will be equal :-

 \sf \implies 3x + 2 = - 3

 \sf \implies 3x = - 3 - 2

 \sf \implies 3x = - 5

 \sf \implies x = - \frac{5}{3}

 \boxed{\sf x = - \frac{5}{3}}

 \sf \therefore \: value \: of \: x = - \frac{5}{3}

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