SOLUTION: e^(2x)-5e^x+4=0 solve the equation x= smaller value x=larger value

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Question 979806: e^(2x)-5e^x+4=0
solve the equation
x= smaller value
x=larger value
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is a quadratic equation if you
write it like this:
+%28+e%5Ex+%29%5E2+-+5%2A%28+e%5Ex+%29+%2B+4+=+0+
For now, I'll say: +z+=+e%5Ex+
+z%5E2+-+5z+%2B+4+=+0+
By inspection:
+%28+z+-+4+%29%2A%28+z+-+1+%29+=+0+
+z+=+4+
+z+=+1+
-------------
+z+=+e%5Ex+
and
+e%5Ex+=+4+
+x+=+ln%284%29+ ( larger value )
and
+e%5Ex+=+1+
+x+=+ln%281%29+ ( smaller value )