1.
a=-lg5
b=-lg7
ab=lg7*lg5
選A
2.
0.7781=lg2+lg3=lg6
-2=lg0.01
所以lgx=lg0.01+lg6=lg0.06
x=0.06
3.
a^x=b^y=c^z 取對(duì)數(shù)
lga^x=lgb^y=lgc^z
xlga=ylgb=zlgc
設(shè)xlga=ylgb=zlgc=t
則1/x=lga/t, 1/y= lgb/t, 1/z=lgc/t
1/x+1/y+1/z=lga/t +lgb/t + lgc/t =（lga+lgb+lgc）/t=lgabc/t=0
lgabc=0
abc=1
4.
關(guān)于x的方程x^2-2x+lg(c^2-b^2)-2lga+1=0有等根,所以delta=0
4-4[lg(c^2-b^2)-2lga+1]=0
1-lg(c^2-b^2)+lga^2-1=0
lga^2=lg(c^2-b^2)
a^2=c^2-b^2
a^2+b^2=c^2
所以為直角三角形
5.
f(-1)=-2
(-1)^2-(lga+2)+lgb=-2
lgb=lga-1
對(duì)一切實(shí)數(shù)x都有f(x)>=2x，即 f(x)-2x>=0 恒成立,將lgb=lga-1代入后整理得
x^2+(lga+2)x+lga-1-2x>=0
x^2+lga*x+lga-1>=0
所以，delta<=0 ,則
(lga)^2-4(lga-1)<=0
(lga-2)^2<=0
所以lga=2
a=100
lgb=1
f(x)=x^2+4x+1=(x+2)^2-3
所以a=100
函數(shù)在x=-2時(shí)取到最小值-3