log5(1+√6)+log2(-1+√2)=a.则log5(-1+√6)+log2(1+√2)=?√=根号.
问题描述：
log5(1+√6)+log2(-1+√2)=a.则log5(-1+√6)+log2(1+√2)=?
√=根号.
答
注意到 (-1+√6)(√6+1)=6-1=5 => -1+√6=5/(1+√6)
(1+√2)(-1+√2)=2-1=1 => 1+√2 =1/(-1+√2)
log5(-1+√6)+log2(1+√2)
=log5[5/(1+√6)] + log2[1/(-1+√2)]
=log5(5)-log5(1+√6)-log2(-1+√2)
=1-a