Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\)
A
\(\frac{2}{3}\)
B
\(\frac{1}{2} \log 2\)
C
\(\frac{3}{2}\)
D
\(\log 2\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{\log\sqrt{8}}{\log 4 - \log 2} = \frac{\log 8\frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{8 \frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{\frac{1}{2} \log 2^3}{\log 2}\)
= \(\frac{3}{2} \frac{\log 2}{\log 2}\)
= \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #36368)