To solve this logarithmic equation, we can rewrite it using the property of logarithms that states log_a(b) = c is equivalent to a^c = b.

First, we can rewrite the equation as:

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

Next, we can rewrite the left side of the equation using the power rule of logarithms, which states that n*log_a(b) = log_a(b^n):

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

Now, we can remove the logarithms from both sides of the equation by raising 1/2 to the power of each side:

1/2^2 = 2x^2-x

This simplifies to:

1/4 = 2x^2 - x

Rearranging the equation, we get:

2x^2 - x - 1/4 = 0

Now, we can factor this quadratic equation by using the quadratic formula or by standard factorization.

The equation factors to:

(2x - 1/2)(x + 1/2) = 0

Therefore, the solutions are:

2x - 1/2 = 0 OR x + 1/2 = 0

2x = 1/2 OR x = -1/2

x = 1/4 OR x = -1/2

Therefore, the solutions to the equation are x = 1/4 and x = -1/2.