求值:log(√2 -1)(3+2√2)=___

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/22 17:41:39
求值:log(√2-1)(3+2√2)=___求值:log(√2-1)(3+2√2)=___求值:log(√2-1)(3+2√2)=___原式=[log(√2+1)(3+2√2)]/[log(√2+1

求值:log(√2 -1)(3+2√2)=___
求值:log(√2 -1)(3+2√2)=___

求值:log(√2 -1)(3+2√2)=___
原式=[log(√2+1)(3+2√2)]/[log(√2+1)(√2-1)]
=2/[log(√2+1)(√2-1)]
1/(√2+1)=√2-1
所以log(√2+1)(√2-1)=-1
原式=-2

=log(√2 -1) (1+√2)^2
=log(1+√2) 1/(1+√2)^2
=-2

-2.230980187...........

因为3+2√2=(√2 +1)^2
√2 +1=1/(√2 -1)
所以3+2√2=(√2 -1)^(-2)
所以原式等于-2