Starting equation: ( 1
9
) x + 1 = 81
Re-write 1
9
as 3-2, and
Also re-write the right side as 34;
The above two revisions result in this equation:

(3- 2)x+1 = 34
or
3- 2x - 2 = 34
If the powers are equal, and the bases (here, 3) are equal
then the exponents must also be equal:
- 2x - 2 = 4
- 2x = 6
x = -3
See Rules for exponents?