1.lga+lgb=lgab=1 ab=10 lgalgb=m
△=(lga)^2+4(1+lga)=(lga+2)^2=0 lga=-2
a=0.01 b=1000 m=-2*3=-6
2.题应该是f(x)=x^2+(lga+2)x+lgb吧
f(-1)=1-lga-2+lgb=lgb/a-1=-2 b/a=0.1 b=10a
f(x)=x^2+(lga+2)x+lgb≥2x x^2+lga*x+lgb≥0
△=(lga)^2-4lgb≤0 (1-lgb)^2≤0 b=10 a=1
3.洗一次剩1/4 洗两次剩1/4-1/4*3/4=1/16 洗三次剩1/16*(1-3/4)=1/64
(1/4)^n=(1/2)^2n≤1%
2^(-2n)≤0.01 两边同时取对数 -2nlg2≤-2 n≥1/lg2 n≥3.322
所以至少洗4次
4.lgxy=lg(x-2y)^2 xy=(x-2y)^2 x>0 y>0 x>2y
x^2-5xy+4y^2=0 同除以y^2,得(x/y)^2-5x/y+4=0 (x/y-1)(x/y-4)=0
x/y=1(舍)或x/y=4
log√2(x/y)=4
5.x=a^2=b=c^4 a=c^2,logabcX=logc^7X=4/7