Algebra opertions can't solve that. You can only do that
with a graphing calculator:

The solution above has the ln graph incorrectly drawn.

2 ln (x-1) > e^(x-4) - 2

Graph y = left side and y = right side

Graph y = 2 ln(x-1) as a green curve

Graph y = e^(x-4) as a blue curve



Use the intersection feature of your graphing 
calculator to find the two points
where they cross.  They are 

(1.3815389,-1.927085) and (5.6216649, 3.06151) 

The green curve is greater (higher) than the blue curve 
only between those points, so the x-values for which it 
is greater is on the interval 

(1.3815389, 5.6216649)

That's the only way to find the solution.

Edwin