x=2+ln(1-x)

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).

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-7.5,7.5,-5,5,1,1,1,1,1,300,200,func,ln(1-x),null,0,0,,,black,1,none,func,x-2,null,0,0,,,orange,2,none"/>

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].