x =

ln (x-1)(x+2) = 1;

(x-1)(x+2) = e;

x^2 + x - 2 - e = 0;

x_1 =( -1 + sqrt{1 + 8 + 4e})/2 = (-1 +sqrt{9 + 4e})/2 = 1.7290 and

x_2 =( -1 - sqrt{1 + 8 + 4e})/2 = (-1 -sqrt{9 + 4e})/2 = -2.7290 (the second root is < -2 and is not valid).

Answer: x = 1.7290

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