4^x+6^x=9^x
(4/6)^x+1=(9/6)^x
(2/3)^x+1=(3/2)^x
((2/3)^x)^2+(2/3)^x-1=0
设(2/3)^x=a
则：a^2+a-1=0,a>0
a=(√5-1)/2
即：(2/3)^x=(√5-1)/2
x=log(2/3)[(√5-1)/2]