Question

(1/3)^5x+6=9^x-1

Answer 1

Do you mean
\[\left( \frac 1 3\right)^{5x +6} = 9^{x-1}
\]
If this is the case \[ x= - \frac 4 7
\]

Answer 2

to elaborate a little bit more, you need to get the bases to look the same:
(1/3) can be thought of as 3^-1
9 can be thought of as 3^2

so
when the bases are the same you can just eqaute the eponents
now you can just solve for x...