1) To solve the equation Log0.2(x^2 + 4x) = -1, we need to rewrite the equation in exponential form:
0.2^(-1) = x^2 + 4x
5 = x^2 + 4x

Now, let's solve for x by setting the equation equal to zero:
x^2 + 4x - 5 = 0

(x + 5)(x - 1) = 0

This gives us x = -5 or x = 1 as the solutions.

2) To solve the equation Log3 (1/x) + Log3 (sqrt(x)) = -1, we can combine the logs using the product rule of logarithms:
Log3[(1/x) * sqrt(x)] = -1

Log3(1) = -1

3^(-1) = 1

Therefore, x = 1 is the solution to the equation.