Question

2．计算：$\frac{lg3+\frac{2}{5}lg9+\frac{3}{5}lg\sqrt{27}-lg\sqrt{3}}{lg81-lg27}$．

Answer 1

分析 先利用对数的运算性质，将式子中所有项的真数均化为3，再合并“同类对数式“，约分可得答案．

解答 解：$\frac{lg3+\frac{2}{5}lg9+\frac{3}{5}lg\sqrt{27}-lg\sqrt{3}}{lg81-lg27}$=$\frac{lg3+\frac{2}{5}lg{3}^{2}+\frac{3}{5}lg{3}^{\frac{3}{2}}-lg{3}^{\frac{1}{2}}}{lg{3}^{4}-lg{3}^{3}}$=$\frac{lg3+\frac{4}{5}lg{3}^{\;}+\frac{9}{10}lg{3}^{\;}-\frac{1}{2}lg{3}^{\;}}{4lg{3}^{\;}-3lg{3}^{\;}}$=$\frac{\frac{11}{5}lg3}{lg3}$=$\frac{11}{5}$

点评 本题考查的知识点是对数的运算性质，熟练掌握对数的运算性质，是解答的关键．