Math, asked by shifin1696, 11 months ago

2 to the power of x-1 + 2to the power of x+1 is equal to 320

Answers

Answered by Billina
0

Step-by-step explanation:

so ,.......

what to do.......

Answered by Salmonpanna2022
1

Step-by-step explanation:

 \bf \underline{Given-} \\

 \sf{ {2}^{x - 1} +  {2}^{x + 1}  = 320  } \\

 \bf \underline{To \: find-} \\

\textsf{the value of x = ?}\\

 \bf \underline{Solution-} \\

\textsf{We have,}\\

 \sf{ {2}^{x + 1} +  {2}^{x - 1}  = 320  } \\

 \sf{ \Rightarrow \:  {2}^{x}  \: . \:  {2}^{1} +   {2}^{x} \: .   \: {2}^{ - 1}  = 320} \\

 \sf{ \Rightarrow \:  {2}^{x}  \bigg(2 +  \frac{1}{2} \bigg) = 320 } \\

 \sf{ \Rightarrow \:  {2}^{x} \times  \frac{5}{2} = 320  }  \\

 \sf{ \Rightarrow \:  {2}^{x}  =  \frac{320 \times 2}{5} } \\

 \sf{ \Rightarrow \: {2}^{x}   =  \cancel{\frac{ {640}^{128} }{5} } } \\

 \sf{ \Rightarrow \:  {2}^{x}  = 128} \\

 \sf{ \Rightarrow \:  {2}^{x}  = {2}^{7} } \\

 \sf{ \Rightarrow \:  x =7} \\

 \bf \underline{Answer-} \\

 \bf{  \underline{Hence, the \:  value \:  of \: x \: is \: 7.}} \\

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