Solve the equation log(2) [x(x-1)]=1

First, we'll impose the constraints of existence of
logarithm:

x(x-1)>0

The
range of admissible values for x is (1 ; +infinite).

We'll
solve the equation by taking anti-logarithm:

x(x-1) =
2^1

We'll remove the
brackets:

x^2 - x - 2 =
0

We'll apply quadratic
formula:

x1 = [1 + sqrt(1 +
8)]/2

x1 = (1+3)/2

x1 =
2

x2 = -1

Since the second
value of x doesn't belong to (-1; +infinite), we'll reject
it.

We'll accept as solution of equation x =
2.