Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

viniterranova Group Title

Find the value of x and y in this system of equations. x^y=1/y^2 and y^x=1/sqrt(x).

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. sriramkumar Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[x ^{y}=1\div y ^{2} and y ^{x}=1/\sqrt{x} \] u mean??

    • 2 years ago
  2. estudier Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    From the second one, can I say that y^2 = 1/sqrt2...

    • 2 years ago
  3. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok. Keep going.

    • 2 years ago
  4. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    It´s right.

    • 2 years ago
  5. estudier Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So that gives you y and you can sub in the first to get x...

    • 2 years ago
  6. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I solved this question before, but i can´t remember all the steps.

    • 2 years ago
  7. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    May you show me, how?

    • 2 years ago
  8. ash2326 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    @viniterranova Let's continue, would you mind showing me your work?

    • 2 years ago
  9. ujjwal Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    From the second i can say that y=1

    • 2 years ago
  10. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I mad x^y = y.

    • 2 years ago
  11. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So, if x^y=y I got the following expression. y= 1/y^2.

    • 2 years ago
  12. ujjwal Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't know how you got these.. But i am sure they (your above expressions) will still give correct answer since i get y=1 from 2nd expression!!

    • 2 years ago
  13. ash2326 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I know you are substituting but don't use the same variable \[x^y=y\] This will be troublesome, use another variable, if you want to but I don't see how it'd help @viniterranova

    • 2 years ago
  14. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks ash2326.

    • 2 years ago
  15. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    If I mad x^y=y, and rewriting the expressoin, i can got y-1/y^2=0. What do they think?

    • 2 years ago
  16. ash2326 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    How could you use the same variable "y"? it's defined differently. I have something. Let me show you

    • 2 years ago
  17. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok.

    • 2 years ago
  18. ash2326 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[x^y=\frac{1}{y^2}\] \[y^x=\frac{1}{\sqrt x}\] Take log both sides, for both the equations \[y\log x=-2\log y\] \[x\log y=-\frac 1 2\log x\] multiply both the equations, we would get \[xy\log x \times \log y=\log x \times\log y\] or \[xy=1\] We have the equation \[y\log x=-2\log y\] put x=1/y \[y\log{\frac 1y}=-2\log y\] we get \[y\times ( -\log y)=-2\log y\] \[y=2\] so \[x=\frac 12\]

    • 2 years ago
  19. ash2326 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    @viniterranova do you get this?

    • 2 years ago
  20. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[y\times ( -\log y)=-2\log y\]gives y=1 and y=2 ------

    • 2 years ago
  21. ash2326 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes @mukushla I missed that then y=1 and x=1

    • 2 years ago
  22. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    neat sol

    • 2 years ago
  23. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Great.

    • 2 years ago
  24. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    It´s rigth.

    • 2 years ago
  25. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I got y=1 and x= 1 in another way.

    • 2 years ago
  26. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i think x=1/2 and y=2 from xy=1 if x=1/2 then y/2=1 y=2 ans

    • 2 years ago
  27. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    from y log x =-2log y sub x=1/y y log(1/y)=-2log y y(-log y)=-2log y dividing both sides by -log y gives y=-2log y/(-log y) y=2 ans..... and from xy=1 2x=1 then x=1/2 ans ....

    • 2 years ago
  28. viniterranova Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks everyone for the help.

    • 2 years ago
  29. mark_o. Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok yw, have fun....

    • 2 years ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.