Solve: \(5^{x-2} \times 3^{2x-3} = 135\)
Solution
\[ 5^{x-2} \times 3^{2x-3} = 135 \]
\[ \Rightarrow 5^{x-2} \times 3^{2x-3} = 5 \times 3^3 \]
\[ \Rightarrow \frac{5^x}{5^2} \times \frac{3^{2x}}{3^3} = 5 \times 3^3 \]
\[ \Rightarrow \frac{5^x \cdot 3^{2x}}{5^2 \cdot 3^3} = 5 \cdot 3^3 \]
\[ \Rightarrow 5^x \cdot 3^{2x} = 5^3 \cdot 3^6 \]
\[ \Rightarrow (5 \cdot 3^2)^x = (5 \cdot 3^2)^3 \]
\[ \Rightarrow 45^x = 45^3 \]
\[ \Rightarrow x = 3 \]
Final Answer:
\[ \boxed{x = 3} \]