Math, asked by apoorvanayak1306, 10 months ago


if  {2}^{5x}  \div  {2}^{x}  =  \sqrt[5]{32} find \: the \: value \: of \: x

Answers

Answered by MaIeficent
16

Step-by-step explanation:

{\red{\underline{\underline{\bold{Given:-}}}}}

  •  {2}^{5x}  \div  {2}^{x}  =  \sqrt[5]{32}

{\blue{\underline{\underline{\bold{To\:Find:-}}}}}

  • The value of x

{\green{\underline{\underline{\bold{Solution:-}}}}}

 \frac{ {2}^{5x} }{ {2}^{x} }  =  \sqrt[5]{32}  \:  \:  \:  \: ( \therefore \frac{ {a}^{m} }{ {a}^{n} }  =  {a}^{m - n} )  \\  \\  \implies {2}^{5x - x}  =  \sqrt[5]{32}  \\  \\ 32 \: can \: be \: written \: as \: 2 \times 2 \times 2 \times 2 \times 2 =  {2}^{5}  \\  \\  \implies {2}^{4x}  =  \sqrt[5]{ {2}^{5} }  \\  \\  \implies {2}^{4x}  =   { ({2}^{5} )}^{ \frac{1}{5} }  \:  \:  \:  \: ( \therefore  \: if \: \sqrt[n]{a}  =  {a}^{ \frac{1}{n} }) \\  \\  \implies {2}^{4x}  = 2 \\  \\  \implies 4x = 1 \:  \:  \:  \: ( \therefore \: if \:  {a}^{m}  =  {a}^{n}  \: then \: m = n)

\boxed{\implies x = \frac{1}{4}}

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