y=log(8)x=1/3*log(2)x
设直线方程为y=kx,与log(8)x交点(x1,kx1),(x2,kx2)
kx1=log(8)x1,kx2=log(8)x2
分别过M,N作y轴的平行线与函数y=log(2)x的图像交于P,Q
则P,Q横坐标分别为x1,x2
纵坐标分别为
log(2)x1=3log(8)x1=3kx1,
log(2)x2=3log(8)x2=3kx2
故P(x1,3kx1),Q(x2,3kx2)
过P,Q的直线方程为y=3kx,很明显,也经过原点
故O,P,Q三点共线