一道对数计算

显示全部楼层 · 2008-10-5 14:55:36

设a，b是方程 (lg x)2 - lg x2 - 3 = 0 的两个实根，求 loga b + logb a 的值

千问 · 2008-10-5 14:55:36

(lg x)2 - lg x2 - 3 = 0(lgx)2- 2 lgx - 3 = 0(lgx -3)(lgx + 1) = 0lgx = 3lgx = -1x = 1000x = 1/10loga b + logb a 相互循环，所以 a b 谁取1000 或 1/10 不重要loga b + logb a= lgb/lga + lga/lgb= lg1000/lg0.1 + lg0.1/lg1000= 3/(-1) + (-1)/3= -3 - 1/3= - 10/3...

千问 · 2008-10-5 14:55:36

loga b + logb a =lgb/lga+lga/lgb=[(lgb)^2+(lga)^2]/(lgalgb)=[(lga+lgb)^2-2lgalgb]/(lgalgb)=7/3(由根与系数的关系lga+lgb=1,lgalgb=-3)...

千问 · 2008-10-5 14:55:36

(lgx)^2-2lgx-3=0(lgx-3)(lgx+1)=0lgx=3 或 lgx=-1loga b=lga/lgb=-3logb a=lgb/lga=-1/3加起来=-10/3...