$\log (x+14)=\log x+\log 14$

Step 1 ：The given equation is $\log (x+14)=\log x+\log 14$.

Step 2 ：We can use the properties of logarithms to simplify this equation. Specifically, we can use the property $\log a + \log b = \log (ab)$ to rewrite the right side of the equation as $\log (14x)$.

Step 3 ：Setting the two sides of the equation equal to each other, we get $x+14 = 14x$.

Step 4 ：Solving this equation for $x$, we find that $x = \frac{14}{13}$.

Step 5 ：So, the solution to the equation $\log (x+14)=\log x+\log 14$ is $x = \frac{14}{13}$.

Step 6 ：Final Answer: \(\boxed{\frac{14}{13}}\)