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

 Jun 26, 2020
 #1
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Solve for x over the real numbers:
2^(2 x + 3) = 14

Take the logarithm base 2 of both sides:
2 x + 3 = log(14)/log(2)

Subtract 3 from both sides:
2 x = log(14)/log(2) - 3

Divide both sides by 2:
 
x = log(14)/(2 log(2)) - 3/2    OR:   x≈0.403677

 Jun 26, 2020
 #2
avatar+30647 
+1

22x+3 = 22x.23 = 8.22x = 8.(2x)2

 

So  8.(2x)2 = 14

 

(2x)2 = 14/8

 

2x = sqrt(14/8)

 Jun 26, 2020

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