Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\)

Answer Details

We can start by simplifying the numerator first: \begin{align*} \log \sqrt{8} &= \log \left(\sqrt{4}\cdot\sqrt{2}\right) \\ &= \log 4 + \log \sqrt{2} \\ &= 2 + \frac{1}{2} \log 2 \end{align*} Similarly, we can simplify the denominator: \begin{align*} \log 4 - \log 2 &= \log\frac{4}{2} \\ &= \log 2 \end{align*} Now we can substitute these simplified expressions back into the original expression: \begin{align*} \frac{\log \sqrt{8}}{\log 4 - \log 2} &= \frac{2 + \frac{1}{2} \log 2}{\log 2} \\ &= \frac{2}{\log 2} + \frac{1}{2} \\ &= \boxed{\frac{3}{2}} \end{align*} Therefore, the correct option is (c) \(\frac{3}{2}\).