SOLUTION: for what values of x is : 2 ln (x-1) > e^(x-4) - 2

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Question 80987: for what values of x is :
2 ln (x-1) > e^(x-4) - 2

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2 ln (x-1) > e^(x-4) - 2
This is one equation you cannot solve analytically.
Graph the left side and the right side separately
and determine over what x-interval the left side
is greater than the right side:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C2ln%28x-1%29%2Ce%5E%28x-4%29-2%29
I get 1.3815 < x < 5.622
Comment: This site graphs the left side properly
but does not do a good job with the right side.
Hopefully you have a graphing calculator.
==========
Cheers,
Stan H.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

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

graph%28300%2C300%2C-2%2C8%2C-5%2C5%2C0%2C2%2Aln%28x-1%29%2C+%28exp%28x-4%29%29-2%29

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