Simplify: \(\frac{\log \sqrt{27}}{\log {81}}\)
- 1/6
-
3/8
- 1/2
- 3/4
- 6
The correct answer is: B
Explanation
\(\frac{\log \sqrt{27}}{\log 81}\)
= \(\frac{\log \sqrt{3^3}}{\log 3^4}\)
= \(\frac{\log 3^{\frac{3}{2}}}{\log 3^4}\)
= \(\frac{\frac{3}{2} \log 3}{4 \log 3}\)
= \(\frac{\frac{3}{2}}{4}\)
= \(\frac{3}{8}\)