log3(3^x-1)*log(3^(x-1)-1/3)=2
令log3(3^x-1)=t,则log3(3^(x-1)-1/3)=log3[(3^x-1)/3]=log3(3^x-1)-1=t-1
则原方程即
t(t-1)=2
解得t=-1或t=2
于是log3(3^x-1)=-1或log3(3^x-1)=2
3^x=4/3或3^x=10
x=log3 (4/3) 或x=log3 (10)