What is the meaning of LN in the function y = ln (x-1)?

What is the meaning of LN in the function y = ln (x-1)?

Denotes the sign of a logarithmic function with E as the base

Given the function f [x] = ln x (x ≠ 0), G (x) = 1 / F '(x) + AF' (x) (x ≠ 0), find (1) if x is not equal to
Given the function f [x] = ln x (x ≠ 0), the function g (x) = 1 / F '(x) + AF' (x) (x ≠ 0)
Find (1) when x is not equal to 0, find the expression of function y = g (x)
(2) If a > 0 is, the minimum value of function y = g (x) on (0, + ∞) is 2
(3) Under the condition of (2), find the area enclosed by the image of the line y = 2 / 3x + 7 / 6 and the function y = g (x)

1.f '(x)=1/x g(x) = x+a/x,（x≠0）
2.a>0,g '(x) = 1- a/x²,z
Get the minimum value g (√ a) = 2 √ a = 2, a = 1 in x = √ a
3. G (x) = x + 1 / x, straight line y = (2 / 3) x + (7 / 6), their intersection points (2,5 / 2) and (3 / 2,13 / 6)
Area s = ∫ [(x + 1 / x) - (2x / 3 + 7 / 6)] DX: 3 / 2 - > 2
= (x² /6 + lnx - 7x /6) | x=2 - (x² /6 + lnx -7x /6) | x=3/2
= ln(4/3) - 7/24

Let f (x) = [ln (1-x)] / X when x is not equal to 0, and f (x) = - 1 when x = 0. If the function is differentiable at x = 0, find the derivative value of the function when x = 0

At the segmentation point, the derivative should be determined according to the definition
f'(0)=lim[ln(1-x)+x]/x^2]
According to the law of Robida
Original formula = Lim1 / 2 (x-1) = - 1 / 2