Solve the equation $\log (x+22)+\log (x+1)=2$. If there are two solutions, separate them by a comma. If there is no solution, enter "DNE".
\[
x=
\]

Step 1 ：Combine the two logarithms into one using the property of logarithms that states that the sum of two logarithms (with the same base) is equal to the logarithm of the product of the numbers. This will give us a single logarithm on the left side of the equation.

Step 2 ：Use the property of logarithms that states that if \(\log_b a = c\), then \(b^c = a\) to solve for x.

Step 3 ：The solution from the calculation is in a form that is not easy to interpret. We need to simplify it and check if the solutions are valid (i.e., they don't result in taking the logarithm of a negative number).

Step 4 ：The solution to the equation \(\log (x+22)+\log (x+1)=2\) is \(x = \boxed{-0.653846022717055}\).