? QUESTION Write the expression as a single logarithm. \[ 3 \log _{c}(2 y+1)+\frac{1}{2} \log _{c}(y+8) \]

Step 1 ：First, we recall the properties of logarithms. Specifically, we use the property \(a \log_b(c) = \log_b(c^a)\) and \(\log_b(c) + \log_b(d) = \log_b(cd)\).

Step 2 ：Applying the first property to the given expression, we get \(\log_c((2y+1)^3) + \log_c((y+8)^{1/2})\).

Step 3 ：Then, we apply the second property to combine the two logarithms into one, yielding \(\log_c((2y+1)^3 \cdot (y+8)^{1/2})\).

Step 4 ：This is the expression as a single logarithm. We check that this expression is equivalent to the original expression, and find that it is.

Step 5 ：So, the final answer is \(\boxed{\log_c((2y+1)^3 \cdot (y+8)^{1/2})}\).