Question 563953
(1/3)^x+1 = 9^x 
you made a mistake making the bases the same:
9^-2=1/81 so that doesn't work
you want 
9^-(1/2)=1/3
So you get:
9^-(1/2)(x+1) = 9^x 
-(1/2)(x+1) simplifies to -1/2x-1/2 since you have to distribute the negative 1/2

-(1/2)x-1/2=x
Multiply both sides by 2 to clear the fraction
-x-1=2x
add x to both sides
-1=3x
divide both sides by 3
x=-1/3

Difficult problem!