Question

$(\frac{1}{3})^{x-8} = 81$

Answer 1

(1/3)^х-8= 81
(1/3)^х-8= (1/3)^(-4)
х-8=-4
х=-4+8
х= 4

Answer 2

$\displaystyle\bigg(\frac{1}{3} \bigg)^{x-8} =81~;\\\\(3^{-1} )^{x-8} =3^4~;\\\\3^{-x+8} =3^4\Rightarrow \\-x+8=4\Rightarrow\\x=4.$