To solve the given equation, we will first isolate the term inside the parenthesis on the left side of the equation.

2log8(2-log2(x-3)) = 0

Next, we can rewrite the equation in exponential form:

8^0 = 2-log2(x-3)

Since anything raised to the 0 power equals 1, we have:

1 = 2-log2(x-3)

Now we can solve for x:

2-log2(x-3) = 1

-log2(x-3) = -1

Now, we can exponentiate both sides of the equation to get rid of the log:

2^(-1) = x-3

1/2 = x-3

x = 1/2 + 3

x = 3.5

Therefore, the solution to the equation 2log8(2-log2(x-3))=0 is x = 3.5.