Solve the logarithmic equation. Be sure to reject any value of \( x \) that is not in the domain of the original logarithmic expressions. Gi \( 2 \log x-\log 5=\log 405 \) Solve the equation to find the solution set. Select the correct choice below and, if necessary, fill in the answer box to complete you A. The solution set is (Simplify your answer. Use a comma to separate answers as needed.) B. There are infinitely many solutions. C. There is no solution.

To solve the logarithmic equation \( 2 \log x - \log 5 = \log 405 \), we can start by applying the properties of logarithms. First, rewrite \( 2 \log x \) as \( \log x^2 \): \[ \log x^2 - \log 5 = \log 405 \] Using the property \( \log a - \log b = \log \left( \frac{a}{b} \right) \): \[ \log \left( \frac{x^2}{5} \right) = \log 405 \] Since the logarithm function is one-to-one, we can set the arguments equal to each other: \[ \frac{x^2}{5} = 405 \] Now, multiply both sides by 5: \[ x^2 = 2025 \] Taking the square root of both sides, we find: \[ x = 45 \quad \text{or} \quad x = -45 \] However, since logarithms are only defined for positive values, we reject \( x = -45 \). Thus, the solution set is: A. The solution set is \( 45 \).