Write the expression as a single logarithm. \[ \log _{4}(x+9)+\log _{4} x \] $\log _{4}(x+9)+\log _{4} x=\square$ (Simplify your answer.)

Step 1 ：The given expression is \(\log _{4}(x+9)+\log _{4} x\).

Step 2 ：The expression consists of two logarithms with the same base that are being added together.

Step 3 ：According to the properties of logarithms, the sum of two logarithms with the same base is equal to the logarithm of the product of the values inside the logarithms.

Step 4 ：Therefore, we can simplify the given expression by multiplying the values inside the logarithms.

Step 5 ：The simplified expression of the given logarithmic expression is \(\boxed{\log _{4}(x(x+9))}\).