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If $x$ is a real number such that $2^{2x+3}=14$, find $2^x$.

 Apr 27, 2022
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2 ^  ( 2x + 3)  =   14         

 

2^3  * 2^(2x)  =  14

 

8 * 2^(2x)  =  14

 

2^(2x)  = 14/8

 

2^(2x)  =  7/4

 

(2^x)^2  = 7/4      take the sq rt  of both sides

 

2^x  =   sqrt ( 7 )  / 2

 

 

cool cool cool

 Apr 27, 2022

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