Question

${2}^{x + 1} + {2}^{x - 1} = 320$
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Answer 1

$\huge\tt{AnsweR}$

Refer the attachment.

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

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

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

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

$\bf \underline{Solution-}$

$\textsf{We have,}$

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

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

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

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

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

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

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

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

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

$\bf \underline{Answer-}$

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