化简lg2∧(1÷2)+lg2∧(2÷3)+lg2∧(3÷4)…+lg2∧(31÷32)=
问题描述:
化简lg2∧(1÷2)+lg2∧(2÷3)+lg2∧(3÷4)…+lg2∧(31÷32)=
答
利用:log(a)[M]+log(a)[N]=log(a)[MN]
得:
原式=log(2)[(1/2)×(2/3)×(3/4)×…×(31/32)]
=log(2)[1/32]
=-log(2)[32]
=-5