高一数学问题xc

log1/2(9^x-1 -5)=log1/2 3^x-1 -2=????

log1/2[9^(x-1)-5]=log1/2[3^(x-1)-2]-2
log1/2[9^(x-1)-5]=log1/2[3^(x-1)-2]-log1/2(1/2)^2
log1/2[9^(x-1)-5]=log1/2{[3^(x-1)-2]÷(1/4)}
log1/2[9^(x-1)-5]=log1/2{4[3^(x-1)-2]}
9^(x-1)-5=4*3^(x-1)-8
令a=3^(x-1)
则9^(x-1)=a²
所以a²-4a+3=0
a=1,a=3
3^(x-1)=1,则真数3^(x-1)-2<0,不成立
3^(x-1)=3
x-1=1
x=2

因M为AB的中点，所以xM=(xA+xB)/2,3=(-2+xB)/2,xB=8;yM=(yA+yB)/2,0=(1+yB)/2, yB=-1.B坐标为(8,-1).直线AB斜率为kAB=(yB-yA)/(xB-xA)=(-1-1)/(8+2)=-1/5直线MN斜率为kMN=(yM-yN)/(xM-xN)=(0+2)/(3+1)=1/2由平行四边形的性质知MN∥BC∥AD，AB∥CD。因此有：kCN=kDN=kAB,kAD=kBC=kMN.即(yC-yN)/(xC-xN)=(yD-yN)/(xD-xN)=-/5,(yD-yA)/(xD-xA)=(yC-yB)/(xC-xB)=1/2.代入各已知数值：(yC+2)/(xC+1)=(yD+2)/(xD+1)=-/5,(yD-1)/(xD+2)=(yC+1)/(xC-8)=1/2.联立上面两式，可求得xC=4,yC=-3;xD=-6,yD=-1.因此C坐标为（4，-3），D坐标为（-6，-1）.