Question

Find the value of x in the following...give in step by step answer...spam will be reported...​

Answer 1

Step-by-step explanation:

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Answer 2

Given

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

To Find

• $† \sf{Value \: of \: x}$

Solution

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

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

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

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

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

• By Cross multiplying

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

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

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

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

• On Comparing both Sides

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

Verification

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

• Putting x= 0

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

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

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

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

• ★$\small\begin{gathered}\begin{gathered}\\\\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \: \underline{\bf{\blue{More \: Useful \: Formula}}}\\ {\boxed{\begin{array}{cc} \sf \bigstar{a}^{m} \times {a}^{n} = {a}^{m + n} \\ \\ \sf \bigstar{a}^{m} \div {a}^{n} = {a}^{m - n} \\ \\ \sf{\bigstar( {a}^{m} ) ^{n} = {a}^{mn} } \\ \\ {\bigstar\sf a {}^{m} \times {n}^{m} = (ab) ^{m} } \\\\ \sf\bigstar{a}^{0} = 1 \\ \\ \sf \bigstar \: {\dfrac{ {a}^{m} }{ {b}^{m} }= \left( \dfrac{a}{b} \right) ^{m} } \\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$