Question

11．計算${log}_{（\sqrt{2}-1）}$（3+2$\sqrt{2}$）=-2．

Answer 1

分析 化簡3+2$\sqrt{2}$=（1+$\sqrt{2}$）²=（$\frac{1}{\sqrt{2}-1}$）²=（$\sqrt{2}$-1）^-2，從而求對數(shù)即可．

解答 解：∵3+2$\sqrt{2}$=（1+$\sqrt{2}$）²=（$\frac{1}{\sqrt{2}-1}$）²=（$\sqrt{2}$-1）^-2，
∴${log}_{（\sqrt{2}-1）}$（3+2$\sqrt{2}$）=${log}_{（\sqrt{2}-1）}$（$\sqrt{2}$-1）^-2=-2．
故答案為：-2．

點評 本題考查了對數(shù)的化簡與運算，屬于基礎(chǔ)題．