Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Find the value of x and y in this system of equations. x^y=1/y^2 and y^x=1/sqrt(x).
 one year ago
 one year ago
Find the value of x and y in this system of equations. x^y=1/y^2 and y^x=1/sqrt(x).
 one year ago
 one year ago

This Question is Closed

sriramkumarBest ResponseYou've already chosen the best response.0
\[x ^{y}=1\div y ^{2} and y ^{x}=1/\sqrt{x} \] u mean??
 one year ago

estudierBest ResponseYou've already chosen the best response.0
From the second one, can I say that y^2 = 1/sqrt2...
 one year ago

estudierBest ResponseYou've already chosen the best response.0
So that gives you y and you can sub in the first to get x...
 one year ago

viniterranovaBest ResponseYou've already chosen the best response.0
I solved this question before, but i can´t remember all the steps.
 one year ago

viniterranovaBest ResponseYou've already chosen the best response.0
May you show me, how?
 one year ago

ash2326Best ResponseYou've already chosen the best response.2
@viniterranova Let's continue, would you mind showing me your work?
 one year ago

ujjwalBest ResponseYou've already chosen the best response.0
From the second i can say that y=1
 one year ago

viniterranovaBest ResponseYou've already chosen the best response.0
So, if x^y=y I got the following expression. y= 1/y^2.
 one year ago

ujjwalBest ResponseYou've already chosen the best response.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!!
 one year ago

ash2326Best ResponseYou've already chosen the best response.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
 one year ago

viniterranovaBest ResponseYou've already chosen the best response.0
If I mad x^y=y, and rewriting the expressoin, i can got y1/y^2=0. What do they think?
 one year ago

ash2326Best ResponseYou've already chosen the best response.2
How could you use the same variable "y"? it's defined differently. I have something. Let me show you
 one year ago

ash2326Best ResponseYou've already chosen the best response.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 \[x=\frac 12\]
 one year ago

ash2326Best ResponseYou've already chosen the best response.2
@viniterranova do you get this?
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
\[y\times ( \log y)=2\log y\]gives y=1 and y=2 
 one year ago

ash2326Best ResponseYou've already chosen the best response.2
Yes @mukushla I missed that then y=1 and x=1
 one year ago

viniterranovaBest ResponseYou've already chosen the best response.0
I got y=1 and x= 1 in another way.
 one year ago

mark_o.Best ResponseYou've already chosen the best response.0
i think x=1/2 and y=2 from xy=1 if x=1/2 then y/2=1 y=2 ans
 one year ago

mark_o.Best ResponseYou've already chosen the best response.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 ....
 one year ago

viniterranovaBest ResponseYou've already chosen the best response.0
Thanks everyone for the help.
 one year ago
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
 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.