We have to solve the equation log(2) [x(x-1)]=1

As the base of the logarithm is 2 we can rewrite it as:

x(x-1) = 2^1

=> x^2 - x = 2

=> x^2 - x - 2 = 0

=> x^2 - 2x +x - 2 = 0

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

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

So we get x = 2 and x = -1, but as the logarithm of a negative number is not defined we eliminate x = -1

**Therefore x = 2**