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

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wagon23
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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.
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the bear
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(√ 3 )y = y(√ 3 )
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RDKGames
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(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.
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wagon23
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(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?
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ghostwalker
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(Original post by wagon23)
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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.
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wagon23
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(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.
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