Equation Solving

[earnest warren]

How would you solve the attached equation (i.e. find alpha)?
Knowing that alpha < 1

[sonic heath]

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[wicked sage]

Let $e^\alpha =t$ so you get a quadratic equation in t

[toxic silo]

🌈Marijuanette🌈

[earnest warren]

So you want me to solve t - 1/t = 1 ?

[wicked sage]

Yes

Then take log _e of the solutions

See which ones are < 1

[earnest warren]

Okay lemme check this out 🙂

[earnest warren]

Okay so I found two solutions of a polynomial expression, one being negative. So I applied ln on the positive one, which makes circa 0.48. I think it works.

[wicked sage]

I see

I wanted to point something out

Are you aware of the hyperbolic cosine

[stoic yew]

Well, hyperbolic sine would work better here.

[earnest warren]

Is it about the Euler formulas?

[wicked sage]

Yeah nvm

It's really not necessary

[wicked sage]

I forgot which one has the minus

[stoic yew]

Hyperbolic sine.

[wicked sage]

Ok

[earnest warren]

Well I mean I have the Euler formulas in my courses, but never took a look at how it actually works.

[wicked sage]

I see

[earnest warren]

Just a quick question. When you wrote 'log _e', it meant the ln function, right?

[wicked sage]

Yes

[earnest warren]

Okay aight!

[earnest warren]

Thanks for your help!

+close

[potent wind]

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[potent wind]

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