Solve the equation analytically. \[ 3^{2 x-5}=9 \]

Step 1 ：Rewrite the equation in the form of an exponential equation with the same base: \(3^{2x-5}=3^2\)

Step 2 ：Since the bases are the same, equate the exponents and solve for x: \(2x - 5 = 2\)

Step 3 ：Solve the equation to find the value of x: \(x = \frac{7}{2}\)

Step 4 ：Final Answer: The solution to the equation is \(\boxed{x = \frac{7}{2}}\)