Solve: \(4^{2x} = \frac{1}{32}\)
Solution
\[ 4^{2x} = \frac{1}{32} \]
\[ (2^2)^{2x} = 2^{-5} \]
\[ 2^{4x} = 2^{-5} \]
\[ \Rightarrow 4x = -5 \]
\[ \Rightarrow x = -\frac{5}{4} \]
Final Answer:
\[ \boxed{x = -\frac{5}{4}} \]
\[ 4^{2x} = \frac{1}{32} \]
\[ (2^2)^{2x} = 2^{-5} \]
\[ 2^{4x} = 2^{-5} \]
\[ \Rightarrow 4x = -5 \]
\[ \Rightarrow x = -\frac{5}{4} \]
\[ \boxed{x = -\frac{5}{4}} \]