2Log 1/2 = log(2x^2 - x)

Rewrite 1/2 as 2^(-1):

2Log 2^(-1) = log(2x^2 - x)

Apply the power rule of logarithms on the left side:

Log 2^(-2) = log(2x^2 - x)

Now we can drop the logarithms:

2^(-2) = 2x^2 - x

1/4 = 2x^2 - x

Rearrange the equation to set it equal to 0:

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

Now solve the quadratic equation using the quadratic formula:

x = [-(-1) ± sqrt((-1)^2 - 42(-1/4))] / 4
x = [1 ± sqrt(1 + 2)] / 4
x = [1 ± sqrt(3)] / 4

Therefore, the solutions to the equation are:

x = (1 + sqrt(3)) / 4
x = (1 - sqrt(3)) / 4