Question

What is the value of eπ?​

Answer 1

Answer:

In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is eπ, that is, e raised to the power π. Like both e and π, this constant is a transcendental number. This was first established by Gelfond and may now be considered as an application of the Gelfond–Schneider theorem, noting that.

Step-by-step explanation:

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Answer 2

• What is the value of eπ−πe in mathematics?

Can’t Comment on the exact Value but will be a POSITIVE NUMBER for sure.

Proof: Consider a function as $x^y=y^x$

(Equality in equation is not necessary, but it’s just that I derived it in this manner as I thought this assumption to be easy for further manipulations. )

Now on taking xy(th) root on both sides Makes the function as:

$x^(1/x)=y^(1/y)$.

Now Differentiate the function on both sides w.r.t ‘x’.

Find the intervals of increase and decrease.

I think it increases in (-infinity,e)

and decreases in (e,infinity).

Since x=e and y=pi.and the value of function decreases in (e,pi)

so f(e)>f(pi)

So, $e^(1/e)>e^(1/pi).$

or Taking power of e*pi.

It becomes e^pi>pi^e.

• Hence it is a Positive no.✔️