\(\frac{\log \sqrt{27}}{\log \sqrt{81}}\) = \(\frac{\log 27\frac{1}{2}}{81\frac{1}{2}}\) = \(\frac{\log 3\frac{1}{2}}{\log 3^2}\) \(\frac{\frac{3}{2} \log 3}{2 \log 3} = \frac{3}{2} \div \frac{2}{1}\) = \(\frac{3}{2} \times \frac{1}{2}\) = \(\frac{3}{4}\)