log27−log8log3−log2\frac{\log \sqrt{27} - \log \sqrt{8}}{\log 3 - \log 2}log3−log2log27−log8
= log33−log23log3−log2\frac{\log \sqrt{3^3} - \log \sqrt{2^3}}{\log 3 - \log 2}log3−log2log33−log23
= log33/2−log23/2log3\frac{\log 3^{3/2} - \log 2^{3/2}}{\log 3}log3log33/2−log23/2
=32(log3−log2)log3−log2\frac{\frac{3}{2}(\log 3 - \log 2)}{\log 3 - \log 2}log3−log223(log3−log2)
∴32\therefore \frac{3}{2}∴23
