Question

12．log₆3•log₆12+（log₆2）²-27${\;}^{\frac{2}{3}-lo{g}_{3}2}$=-8-${log}_{3}^{2}$．

Answer 1

分析 根据对数的运算性质计算即可．

解答 解：log₆3•log₆12+（log₆2）²-27${\;}^{\frac{2}{3}-lo{g}_{3}2}$
=log₆3•（${log}_{6}^{3}$+${log}_{6}^{4}$）+（log₆2）²-9-${log}_{3}^{2}$
=${{（log}_{6}^{3}）}^{2}$+2${log}_{6}^{3}$${log}_{6}^{2}$+${{（log}_{6}^{2}）}^{2}$-9-${log}_{3}^{2}$
=${{（log}_{6}^{3}{+log}_{6}^{2}）}^{2}$-9-${log}_{3}^{2}$
=-8-${log}_{3}^{2}$，
故答案为：-8-${log}_{3}^{2}$．

点评 本题考察了对数的运算，熟练掌握运算性质是解题的关键，本题是一道基础题．