To solve the equation, we can start by rewriting the equation in exponential form:

3^(Log3(x^2-9x+47)) = 3^3

This simplifies to:

x^2 - 9x + 47 = 27

Now we have a quadratic equation, so we can set it equal to zero and solve for x:

x^2 - 9x + 47 - 27 = 0
x^2 - 9x + 20 = 0

Now we can factor this quadratic equation:

(x - 4)(x - 5) = 0

Setting each factor equal to zero:

x - 4 = 0 or x - 5 = 0
x = 4 or x = 5

Therefore, the solutions to the equation are x = 4 and x = 5.