Find: \(2^{1+x}\), if \(3^{x+1} = 9^{x-2}\)
Solution
\[ 3^{x+1} = 9^{x-2} \]
\[ \Rightarrow 3^{x+1} = (3^2)^{x-2} \]
\[ \Rightarrow 3^{x+1} = 3^{2x-4} \]
\[ \Rightarrow x+1 = 2x-4 \]
\[ \Rightarrow x = 5 \]
\[ 2^{1+x} = 2^{6} \]
\[ = 64 \]
Final Answer:
\[ \boxed{64} \]