f x=4^x+m2^x-6m
=(2^x+m/2)²-m²/4-6m
f x=4^x +m2^x-6m恰有一零点,得
(1)2^x+m/2=0,-m²/4-6m=0
得m=-24
(2) m/2>0,-m²/4-6m0
实数m范围是{-24}∪{m|m>0}