2 log(x) - log(x - 1) = log(x - 2)
log(x²) - log(x - 1) = log(x - 2)
log(x² / (x - 1)) = log(x - 2)
x² / (x - 1) = x - 2
x² = (x - 1) (x - 2)
x² = x² - 3x + 2
0 = -3x + 2
3x = 2
x = 2/3
But notice that 2/3 - 1 = -1/3 < 0, and log(x - 1) is undefined so there are no real solutions.