由题知,
log₂(1-x)/(1+x)=-log0.5x=-log(1/2)x=log₂x,
则(1-x)/(1+x)＞0,-1＜x＜1,
且x＞0,
即0＜x＜1,
又(1-x)/(1+x)=x,
解得x=-1+√2,或x=-1-√2(舍).