To solve this logarithmic equation, we need to first combine the logarithms on the left side using the properties of logarithms:

log3(x-2) + log3(x-4)^2 = 0
log3((x-2)(x-4)^2) = 0

Now, we can rewrite the equation in exponential form:

3^0 = (x-2)(x-4)^2
1 = (x-2)(x-4)^2

Next, let's expand the right side of the equation:

1 = (x-2)(x^2 - 8x + 16)
1 = x^3 - 8x^2 + 16x - 2x^2 + 16x - 32
1 = x^3 - 10x^2 + 32x - 32

Now, we can rearrange the equation to form a cubic equation:

x^3 - 10x^2 + 32x - 32 - 1 = 0
x^3 - 10x^2 + 32x - 33 = 0

This equation does not have a simple solution and will require the use of numerical methods or a graphing calculator to find the real solutions.