3. Chapter 3 (Course Work Solve the logarithmic equation. Be sure to reject any value of \( x \) that is not in the domain of the \( \log (x+8)-\log 2=\log (2 x+3) \) Solve the equation to find the solution set. Select the correct choice below and, if necessary, \( f \) 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 \(\log(x + 8) - \log(2) = \log(2x + 3)\), we can use the properties of logarithms. First, we can combine the logs on the left side: \[ \log\left(\frac{x + 8}{2}\right) = \log(2x + 3) \] By using the property that if \(\log(a) = \log(b)\), then \(a = b\), we get: \[ \frac{x + 8}{2} = 2x + 3 \] Cross-multiply and simplify: \[ x + 8 = 4x + 6 \] Now, rearranging gives: \[ 8 - 6 = 4x - x \] \[ 2 = 3x \] \[ x = \frac{2}{3} \] Now we need to check if this solution is within the domain of the original logs. For \(\log(x + 8)\) to be defined, \(x + 8 > 0\), which is true for \(x = \frac{2}{3}\). For \(\log(2x + 3)\) to be defined, \(2x + 3 > 0\), which is also true for \(x = \frac{2}{3}\). Thus, the solution set is \(\{ \frac{2}{3} \}\). So the correct choice is: A. The solution set is \{ \( \frac{2}{3} \} \}.