Question Write $\log (\sqrt{7} z)$ in expanded form.

Step 1 ：Write \(\log (\sqrt{7} z)\) in expanded form.

Step 2 ：The logarithm of a product can be written as the sum of the logarithms of the individual factors. Therefore, we can write \(\log (\sqrt{7} z)\) as \(\log (\sqrt{7}) + \log (z)\).

Step 3 ：The logarithm of a root can be written as a fraction. Therefore, we can further simplify \(\log (\sqrt{7})\) as \(\frac{1}{2} \log (7)\).

Step 4 ：So, the expanded form of \(\log (\sqrt{7} z)\) is \(\log(z) + \frac{1}{2}\log(7)\).

Step 5 ：Final Answer: \(\boxed{\log(z) + \frac{1}{2}\log(7)}\)