To solve this problem, we can use the properties of logarithms to combine the two logarithmic terms into one.

First, let's rewrite the equation using the properties of logarithms:

log1/2(x^2) - log1/2(x) = 6

Next, we can use the property of logarithms that states: log_b(x) - log_b(y) = log_b(x/y)

Therefore, we can rewrite the equation as:

log1/2(x^2 / x) = 6

Simplify the expression inside the logarithm:

log1/2(x) = 6

Now, since the base of the logarithm is 1/2, we can rewrite the equation in exponential form:

1/2^6 = x

x = 1/64

So, the solution to the equation log1/2(x^2) - log1/2(x) = 6 is x = 1/64.