2logx-log(x-1)=log(x-2)

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.

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