log2{[9^(x-1)-5]/[3^(x-1)-2]=2
[9^(x-1)-5]/[3^(x-1)-2]=2^2
9^(x-1)-5=4[3^(x-1)-2]
令a=3^(x-1),则9^(x-1)=a^2
a^2-5=4(a-2)
a^2-4a+3=0
a=1,a=3
由定义域a^2-5>0,a-2>0
所以a=3
3^(x-1)=3=3^1,x-1=1,x=2