SOLUTION: for the function 'e^2x = e^x + 2', could you please explain how there is only one real answer? We have to explain, using a graph where the functions 'y = e^2x' and 'y = e^x

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: for the function 'e^2x = e^x + 2', could you please explain how there is only one real answer? We have to explain, using a graph where the functions 'y = e^2x' and 'y = e^x      Log On


   

Question 39231: for the function
'e^2x = e^x + 2',
could you please explain how there is only one real answer?
We have to explain, using a graph where the functions
'y = e^2x' and 'y = e^x +2'
are sketched on the same set of axes, why this is so. Thanks alot :)
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+e%5E2x+=+e%5Ex+%2B+2+
+e%5E2x+-+e%5Ex+-+2+=+0+

Let +y=e%5Ex, then
+y%5E2+-+y+-+2+=+0+
(y-2)(y+1) = 0
so y-2=0 or y+1=0
so y = 2 or y = -1

--> +e%5Ex+=+2+ or +e%5Ex+=+-1+
--> x = ln(2) or x = ln(-1)

Put ln(-1) into your calculator...you get an error. So the only answer is x=ln(2).

You need to plot the 2 curves on the one graph. Doing so, you will get that they cross at one point only, the solution point, at a value of x=ln(2).

jon.