# root(3)^Y = Y^root(3), where Y ≠ root(3)

Watch
Announcements
#1
How to solve for Y?

the first part of the question asked to put XY = YX in terms of parametric equations, which was X = t(1/t-1) , Y = t(t/t-1) . But now we working backwards to solve for t which is where am stuck?

i tried
root(3) = t(t/t-1) , but I have no idea how to isolate the t? I tried using natural log both sides then simplifying it but that didn't help me much I was only able to simplify it to
(root(3)/t)t = root(3) or root(3)t = root(3)tt
Is this even the right approach to getting the value of t?

btw The answer should be root(27) for Y.
0
2 years ago
#2
(√ 3 )y = y(√ 3 )
0
2 years ago
#3
(Original post by wagon23)
How to solve for Y?

the first part of the question asked to put XY = YX in terms of parametric equations, which was X = t(1/t-1) , Y = t(t/t-1) . But now we working backwards to solve for t which is where am stuck?

i tried
root(3) = t(t/t-1) , but I have no idea how to isolate the t? I tried using natural log both sides then simplifying it but that didn't help me much I was only able to simplify it to
(root(3)/t)t = root(3) or root(3)t = root(3)tt
Is this even the right approach to getting the value of t?

btw The answer should be root(27) for Y.
That equation is a type of a transcendental equation; you cannot solve it analytically.
0
#4
(Original post by RDKGames)
That equation is a type of a transcendental equation; you cannot solve it analytically.
So in the case of it being a transcendental equation my only option is approximate it via iteration method then? also how were you able to identify it as a transcendental equation?
0
2 years ago
#5
(Original post by wagon23)
...
Since you look to be studying A-level, I think it would be a good idea to post the whole question, or better still link to it, so we can see the original.
0
#6
(Original post by ghostwalker)
Since you look to be studying A-level, I think it would be a good idea to post the whole question, or better still link to it, so we can see the original.
It wasn't a past year question, just a question our teacher gave for those interested in maths.
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### Are you travelling in the Uni student travel window (3-9 Dec) to go home for Christmas?

Yes (117)
28.26%
No - I have already returned home (56)
13.53%
No - I plan on travelling outside these dates (81)
19.57%
No - I'm staying at my term time address over Christmas (40)
9.66%
No - I live at home during term anyway (120)
28.99%