We can rewrite 9^-x as (3^2)^-x, which is equal to 3^-2x. Then we have:
27 = 3^-2x + 5
Subtracting 5 from both sides gives:
22 = 3^-2x
Taking the reciprocal of both sides gives:
3^2x = 1/22
Taking the logarithm of both sides with base 3 gives:
2x = log₃(1/22)
Using the change of base formula, we get:
2x = log(1/22) / log(3)
Simplifying gives:
x = (1/2) * log(22) / log(3) - Answer