Verified answer

3^(x-3)+3^(x-2)+3^(x-1)=13*3^(-2),

3^x / 3^3 + 3^x / 3^2 + 3^x / 3^1 = 13 / 3^2,

3^x (1/27+1/9+1/3) = 13/9,

3^x * 13/27 = 13/9,

3^x=13/9 * 27/13,

3^x = 3,

3^x=3^1,

x=1.