To solve this equation, we first need to isolate the logarithmic term on one side of the equation.

Log3(x2-11x+27) = 2

Using the properties of logarithms, we can rewrite this equation in exponential form:

3^2 = x^2 - 11x + 27

Simplifying:

9 = x^2 - 11x + 27

Rearranging to standard form:

x^2 - 11x + 18 = 0

Now we can factor the quadratic equation:

(x - 2)(x - 9) = 0

Setting each factor to zero:

x - 2 = 0 or x - 9 = 0

So the solutions to the equation are:

x = 2 or x = 9