For what value of $x$ is the following true? \[ \log (x+10)=\log x+\log 10 \] Your answer is: \[ x= \] You may enter the exact value or round to 4 decimal places.

Step 1 ：Given the equation \(\log (x+10)=\log x+\log 10\)

Step 2 ：Using the property of logarithms that the log of a product is the sum of the logs of the individual factors, we can rewrite the right side of the equation as a single logarithm: \(\log (x \cdot 10)\)

Step 3 ：Then, we can use the fact that if \(\log(a) = \log(b)\), then \(a\) must equal \(b\), to solve for \(x\)

Step 4 ：So, we have \(x+10 = 10x\)

Step 5 ：Solving for \(x\), we get \(x = \frac{10}{9}\)

Step 6 ：Final Answer: \(x=\boxed{\frac{10}{9}}\)