Solve: \(3^{x-1} \times 5^{2y-3} = 225\)
Solution
\[ 3^{x-1} \times 5^{2y-3} = 225 \]
\[ \Rightarrow 3^{x-1} \times 5^{2y-3} = 3^2 \times 5^2 \]
\[ \Rightarrow 3^{x-1} = 3^2,\quad 5^{2y-3} = 5^2 \]
\[ \Rightarrow x-1 = 2 \]
\[ \Rightarrow x = 3 \]
\[ \Rightarrow 2y-3 = 2 \]
\[ \Rightarrow 2y = 5 \]
\[ \Rightarrow y = \frac{5}{2} \]
Final Answer:
\[ \boxed{x = 3,\; y = \frac{5}{2}} \]