To solve this equation, we will first simplify the left side by using log rules:

(log base 2 (x) - log base 2 (x^2)) = (x-1)^3

Now, we can use the property of logarithms that states log base a (b) - log base a (c) = log base a (b/c). Applying this property, we get:

log base 2 (x/x^2) = (x-1)^3

Simplifying the left side further, we get:

log base 2 (1/x) = (x-1)^3

Next, we need to convert the logarithmic equation into an exponential form:

2^(x-1)^3 = 1/x

This equation can be solved by taking the reciprocal of both sides:

x = 1/(2^(x-1)^3)

Therefore, the solution of the equation is x = 1/(2^(x-1)^3).