If \(x\) is a real number such that \(2^{2x+3}=14 \), find \(2^x\).
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
22x+3 = 22x.23 = 8.22x = 8.(2x)2
So 8.(2x)2 = 14
(2x)2 = 14/8
2x = sqrt(14/8)
+171 
