A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
2(e^x2)=(e^x)+7... Solve the equation
anonymous
 5 years ago
2(e^x2)=(e^x)+7... Solve the equation

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is that \[2e^{x2} = e^x + 7\]?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, so first off, move all the \(e^x\) terms to one side of the equal sign.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0By adding or subtracting things from both sides.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For example, go ahead and subtract \(e^x\) from both sides and what do you get?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Good. Now lets rewrite that \(e^{x2}\) as the product of two powers of e. Recall that \[a^b * a^c = a^{b+c}\] So what can we rewrite \[e^{x2}\] as?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Correct. So that means that our equation becomes?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right. Now since both terms on the left side have an \(e^x\) factor, we can factor it out in front of the sum. a*b + a*c = a(b+c)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no sure how to right it now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{2}{e^2}(e^x)  e^x = 7\] \[e^x(\frac{2}{e^2}  1)= 7\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Not sure why those fractions aren't showing up right..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But anyway, then you just divide by the second bit leaving only the \(e^x\) on the left side.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You should have \[e^x = \frac{7}{(2e^{2})  1}\] Then you take the ln of both sides.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so... x= ln7/(2ln 2)  ln1 not sure about denominator. Is that correct

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No, you have to take the ln of the whole thing, not the ln of the top divided by the ln of the bottom. If you want to break it up further you can use the property of log of a quotient is subtraction of the log. \[ln[\frac{a}{b}] = (ln\ a)  (ln\ b)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so... x=ln7((2ln2)1) ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think i did something wrong bc u cnt have ln and then a negative. What woudit be then

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It should be: \[x = (ln\ 7)  (ln [2e^{2}  1])\] It cannot be simplified further because we can't do anything with the log of a sum. But you can plug it into your calculator if you like. I think you may have tried to do \((ln\ e^{2})\) which isn't legal in this case, but is legal in other situations. It's not equal to \(ln 2\) though.. \[ln[e^{2}] = 2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks for everything

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it said not real in calculator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hrmph.. That's true actually. \(2e^{2}\) is less than 1, so when you subtract 1 from it you'll have a negative number and you cannot take the ln of a negative.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We must have missed something

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Nope, that's the correct solution to this equation. It has no real soltions.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Solutions rather. Double check what I wrote originally.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what u originaly wrote is corect

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0must be no solutions thanks again
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.