Question

find the value of x if 1/2^x+1/2^x+1/2^x=3
​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

${ \bigstar \: \sf \: \dfrac{1 \: }{ {2}^{x} } + \dfrac{1 \: }{ { 2 }^{x} } + \cfrac{1 \: }{ {2}^{x} } = 3}$

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

$† \sf{the\: value \: of \: x = ?}$

$\bf \underline{Solution-}$

${ \: \: \: \: \: : \implies \: \sf \: \dfrac{1 \: }{ {2}^{x} } + \dfrac{1 \: }{ { 2 }^{x} } + \cfrac{1 \: }{ {2}^{x} } = 3}$

$\bf{Taking \: \: \dfrac{1 \: \: }{2^x} \: Common }$

${ \: \: \: \: \: : \implies \: \sf \: \dfrac{1 \: }{ {2}^{x} } (1 + 1 + 1) = 3}$

${ \: \: \: \: \: : \implies \: \sf \: \dfrac{1 \: }{ {2}^{x} } \times 3 = 3}$

${ \: \: \: \: \: : \implies \: \sf \: \dfrac{3 \: }{ {2}^{x} } = 3}$

$\textsf{By Cross multiplying}$

${ \: \: \: \: \: : \implies \: \sf \: {2}^{x} \times 3 = 3 }$

${ \: \: \: \: \: : \implies \: \sf \: {2}^{x} \times \cancel{ 3}^{1} = \cancel{ 3}^{1} }$

${ \: \: \: \: \: : \implies \: \sf \: {2}^{x} = 1 }$

${ \: \: \: \: \: : \implies \: \sf \: {2}^{x} = {2}^{0} }$

$\textsf{On Comparing both Sides}$

${ \: \: \: \: \: : \implies \boxed{\: \bf \: \pink{x = 0} }}$

$\bf \underline{Verification-}$

$\small{ \small\: \: \: \: \: : \implies \: \sf \: \dfrac{1 \: }{ {2}^{x} } + \dfrac{1 \: }{ { 2 }^{x} } + \cfrac{1 \: }{ {2}^{x} } = 3}$

Putting x= 0

$\small{ \small \: \: \: \: \: : \implies \: \sf \: \dfrac{1 \: }{ {2}^{0} } + \dfrac{1 \: }{ { 2 }^{0} } + \cfrac{1 \: }{ {2}^{0} } = 3}$

$\small{ \small \: \: \: \: \: : \implies \: \sf \: \dfrac{1 \: }{1 } + \dfrac{1 \: }{ 1 } + \cfrac{1 \: }{ 1 } = 3}$

$\small{ \small \: \: \: \: \: : \implies \: \sf \: 1 + 1 + 1 = 3}$

$\small{\small \: \: \: \: \: : \implies \: \sf \: 3= 3 \: \:_{ \mathfrak{ \green{verified}}}}$