Question

一道高二数学题

若a>1,0<b<1,则log以a为底b的对数+log以b为底a的对数的范围？
答案是≤负2

Answer 1

a>1 lga>0
0<b<1 lgb<0
k=lgb/lga<0
log(a)b+log(b)a
=lgb/lga+lga/lgb
=k+1/k
=-(-k+1/(-k))
<=-2