To solve this type of equation, that is called transcendental equation, we'll have to isolate the logarithm function to one side, and the linear equation to the other side, such as:
x - 2 = ln(1 - x)
Now, we'll draw the graphs of the linear equation x - 2 and logarithmic equation ln(1-x).
The graph of the linear function x - 2 is the orange line, whose intercepting points to x and y axis are: (2 ; 0) and (0 ; -2).
The graph of the logarithmic function is the black curve that is passing through the origin (0 ; 0).
The solution of the equation is the intercepting point of the graphs. To determine x coordinate we'll have to draw a perpendicular from intercepting point to x axis.
The solution of the transcedental equation is found in the closed interval [0 ; 1].