Simplify \(\frac{\log \sqrt{27}}{\log \sqrt{81}}\)
- 3
- 2
- \(\frac{3}{2}\)
-
\(\frac{3}{4}\)
The correct answer is: D
Explanation
\(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) = \(\frac{\log 27\frac{1}{2}}{81\frac{1}{2}}\)= \(\frac{\log 3\frac{1}{2}}{\log 3^2}\)
\(\frac{\frac{3}{2} \log 3}{2 \log 3} = \frac{3}{2} \div \frac{2}{1}\)
= \(\frac{3}{2} \times \frac{1}{2}\)
= \(\frac{3}{4}\)