(1)证明假设z为纯虚数,则有log2(x2-3x-3)=0,

　　且log2(x-3)≠0,即x2-3x-3=1,

　　解得x=-1或x=4.

　　当x=-1时,log2(x-3)无意义;

　　当x=4时,log2(x-3)=0与log2(x-3)≠0矛盾,

　　所以复数z不能是纯虚数.

(2)解由题意,得{■(x^2 "-" 3x"-" 3>0"," @x"-" 3>0"," @log_2 "(" x^2 "-" 3x"-" 3")" <0"," @log_2 "(" x"-" 3")" <0"," )┤解得 (3+√21)/2

(3)解由题意,得log2(x2-3x-3)-2log2(x-3)+1=0,解得x=√15 或x=-√15(舍去),

　　即当x=√15 时,点Z在直线x-2y+1=0上.