Simplify \(\frac{\log \sqrt{27}}{\log \sqrt{81}}\)
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Correct Answer: Option D
Explanation:
\(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) = \(\frac{\log 27\frac{1}{2}}{81\frac{1}{2}}\)
= \(\frac{\log 3\frac{1}{2}}{\log 3^2}\)
\(\frac{\frac{3}{2} \log 3}{2 \log 3} = \frac{3}{2} \div \frac{2}{1}\)
= \(\frac{3}{2} \times \frac{1}{2}\)
= \(\frac{3}{4}\)
\(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) = \(\frac{\log 27\frac{1}{2}}{81\frac{1}{2}}\)
= \(\frac{\log 3\frac{1}{2}}{\log 3^2}\)
\(\frac{\frac{3}{2} \log 3}{2 \log 3} = \frac{3}{2} \div \frac{2}{1}\)
= \(\frac{3}{2} \times \frac{1}{2}\)
= \(\frac{3}{4}\)