Solve for $x$ : \[ \log (x)+\log (x+3)=5 \] \[ x= \] You may enter the exact value or round to 4 decimal places.

Step 1 ：Given the equation \(\log (x)+\log (x+3)=5\)

Step 2 ：We can combine the two logarithms on the left side of the equation using the property of logarithms that states that the sum of the logarithms of two numbers is equal to the logarithm of the product of those two numbers. This gives us \(\log (x(x+3))=5\)

Step 3 ：We can then use the property of logarithms that states that if \(\log_b(a) = c\), then \(b^c = a\) to solve for x. This gives us \(x(x+3)=10^5\)

Step 4 ：Solving the quadratic equation, we get two solutions. However, we need to check if they are valid (i.e., they don't result in a logarithm of a negative number).

Step 5 ：The valid solution is \(x = 10.7744922136346\)

Step 6 ：Final Answer: The solution to the equation is \(\boxed{10.7745}\)