Solve: \(2^{2x} – 2^{x+3} + 2^4 = 0\)
Solution
\[ 2^{2x} – 2^{x+3} + 16 = 0 \]
\[ \text{Let } 2^x = t \]
\[ \Rightarrow t^2 – 8t + 16 = 0 \]
\[ \Rightarrow (t – 4)^2 = 0 \]
\[ \Rightarrow t = 4 \]
\[ \Rightarrow 2^x = 4 = 2^2 \]
\[ \Rightarrow x = 2 \]
Final Answer:
\[ \boxed{x = 2} \]