Solve the equation analytically.
\[
3^{2 x-5}=9
\]
Final Answer: The solution to the equation is \(\boxed{x = \frac{7}{2}}\)
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 \(\boxed{x = \frac{7}{2}}\)