把x=2代入
2a^2-7a+3=0
(2a-1)(a-3)=0
a=1/2,a=3
若a=1/2,2(1/2)^(2x-2)-7(1/2)^(x-1)+3=0
则[2*(1/2)^(x-1)-1][(1/2)^(x-1)-3]=0
(1/2)^(x-1)=1/2,(1/2)^(x-1)=3
(1/2)^(x-1)=1/2即x=2
(1/2)^(x-1)=3
x-1=log(1/2)3=-log2(3)
x=1-log2(3)=log2(2/3)
若a=3,2*3^(2x-2)-7*3^(x-1)+3=0
则[2*3^(x-1)-1][3^(x-1)-3]=0
3^(x-1)=1/2,3^(x-1)=3
3^(x-1)=3即x=2
3^(x-1)=1/2
x-1=log3(1/2)=-log3(2)
x=1-log3(2)=log3(3/2)
所以a=1/2,x=log2(2/3)
a=3,x=log3(3/2)
(lga+lgx)(lga+2lgx)=4
(lgx)^2+3lga*lgx+(lga)^2-4=0
x>1则lgx>0
令m=lgx>0
m^2+3lga*m+(lga)^2-4=0
m1>0,m2>0
所以m1+m2=-3lga>0,lga