Solve the following logarithmic equation. \[ \frac{1}{2} \log _{9} x=3 \log _{9} 5 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.) B. There is no solution.

Step 1 ：Given the logarithmic equation \(\frac{1}{2} \log _{9} x=3 \log _{9} 5\)

Step 2 ：First, we can get rid of the fraction in front of the logarithm on the left side of the equation by multiplying both sides of the equation by 2, which gives us \(\log _{9} x=6 \log _{9} 5\)

Step 3 ：Next, we can use the property of logarithms that says that \(\log_b(a^n) = n*\log_b(a)\) to simplify the equation further, which gives us \(\log _{9} x=\log _{9} 5^6\)

Step 4 ：Then, we can use the property of logarithms that says that if \(\log_b(a) = \log_b(c)\), then a = c to find the value of x, which gives us \(x = 5^6\)

Step 5 ：Calculating the value of \(5^6\), we find that \(x = 15625\)

Step 6 ：Substituting \(x = 15625\) into the original equation, we find that both sides of the equation are equal, confirming that \(x = 15625\) is the solution to the equation

Step 7 ：Final Answer: The solution set is \(\boxed{15625}\)