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