To solve this equation, we need to first simplify the expression on the left side:

27^(1-x) = 1/81

Since 1/81 is equivalent to 27^(-2), we can rewrite the equation as:

27^(1-x) = 27^(-2)

Now, we can set the exponents equal to each other:

1-x = -2

Next, solve for x:

1 - x = -2
x = 1 + 2
x = 3

Therefore, the solution to the equation is x = 3.