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

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) (Show Source): You can put this solution on YOUR website!

Let , then

(y-2)(y+1) = 0
so y-2=0 or y+1=0
so y = 2 or y = -1

--> or
--> 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.

RELATED QUESTIONS
HELP: Is my professor unreasonable or am I totally confused? I answered the other 6... (answered by stanbon)

1. Find two positive real numbers whose sum is 40 and whose product is a... (answered by JimboP1977)

Appreciate if you could explain a step by step in detail how to get the answer (C).... (answered by ikleyn,math_tutor2020,greenestamps)

Can you please explain this to me? Thanks so much in advance for your time! If D = {w, (answered by stanbon)

Kathryn and Gaby are enrolled in a university program to study abroad in Spain and then (answered by psbhowmick)

The book is Algebra, 3/e, by K. Elayn Martin-Gay! Determine whether each of the... (answered by checkley75)

I have a student who is coming to me for tutoring for the Praxis I. Initially, I was... (answered by stanbon)

I am looking for the domain and the range for the equation: x^2+y = 10 I thought that (answered by Mathtut,jim_thompson5910,edjones)

Can you please help me solve this question and explain how to solve it shortly? y=3x-5... (answered by Alan3354,Caner1994)