Question

find the value of a
$2 {}^{a + 2} + 2 {}^{2} = 8$


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Answer 1

Answer :-

• a = 0

To Solve :-

${2}^{a + 2} + {2}^{2} = 8$

Step By Step Solution :-

In the given question we have to find the value of a.

So let's do it !!

$\implies\sf 2^{a+2}+2^2=8\\ \\\implies\sf 2^{a+2}=8-2^2\\ \\ \implies\sf2^{a+2}=8-4\\ \\ \implies\sf2^{a+2}=4\\ \\ \implies\sf2^{a+2}=2^2\\\\ \implies\sf Comparing \: powers\\ \\ \implies\sf \: a+2=2\\ \\ \implies\sf \: a=2-2\\ \\\implies\sf a=0$

Therefore a = 0

Check :-

L. H. S.

By substituting the value of a = 0

$\implies \sf{2}^{0 + 2} + {2}^{2} \\ \\ \implies \sf {2}^{2} + {2}^{2} \\ \\ \implies \sf 4 + 4 = 8$

R. H. S.

=> 8

Therefore L. H. S. = R. H. S.

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