lg(x^2+1)-lg(x-2)>1lg(x^2+1)-lg(x-2)>12log25(X)+logx(25)>3
问题描述:
lg(x^2+1)-lg(x-2)>1
lg(x^2+1)-lg(x-2)>1
2log25(X)+logx(25)>3
答
1、lg(x^2+1)-lg(x-2)>1
lg[(x^2+1)/(x-2)]>1
(x^2+1)/(x-2)>10
∵x^2+1》0
∴x-2>0 x>2
解得(x^2+1)/(x-2)>10
x>7或x综上2
2)2log25(X)+logx(25)>3
2log25(X)+[1/log25(x)]>3
lgx/lg5+2lg5/lgx>3
解得x>25或0
答
lg(x^2+1)-lg(x-2)>1lg[(x^2+1)/(x-2)]>1(x^2+1)/(x-2)>10(x^2-10x+21)/(x-2)>0(x-3)(x-7)(x-2)>0232log25(X)+[1/log25(x)]>3设log25(X)=t2t^2-3t+1>0t>1或t1x>25log25(X)