Can you solve this Cambridge Exam Question?

A great question today: 5^x=x. What do you think about this problem?
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[@DedMatveev]

it was brilliant! it took so long to write to show the obvious fact from the very beginning that there are no real solutions!

[@mayaq8324]

No solution, is kind of disappointing :)

[@mikhailkotsarenko6002]

Good explanation, thank you!

[@Coalwarrior2012]

I appreciated your charity. Thank you.

[@mohameddaoud4885]

Your channel and way of explanation is amazing. Could you please start a different "type" of Olympiad questions.

[@RealQinnMalloryu4]

25 5^5 (x ➖ 5x+5) .

[@stvp68]

Thanks for the graph. That’s where I started-could you just use the graph to show there are no real roots instead of doing the algebra?

[@addwithad]

Very nice solution and explanation :)

[@anganaroy-bd1212]

Wth is Lambert w function? Is there any way to solve this problem without using that?

[@thunderpokemon2456]

Noo u cant do it,its product log fun in calculator or use wolframalpha

[@dietrichbuxtehude369]

If you want to show that there is no real solution, you can simply note that 5^x-x -> +infinity when x-> -infinity and x-> +infinity, so the function has a minimum. Derivate it to show that the minimum is reached for x=ln(ln5)/ln5 ; the value of the function at the minimum is (1+ln(ln5))/ln5>0. So 5^x-x is strictly positive for any real value of x, and there is no real solution.

[@anganaroy-bd1212]

@@dietrichbuxtehude369 thanks brother 🫂

[@mzaaimabakar243]

😊

[@60FPSDoraemon]

We find ans by differentiating

[@mistermouse364]

x≈1.0000000001 right?

[@Piotr-d6s]

X = 000000000

[@clairelegendre6445]

excist? exist! ...

[@sawdust195526]

I had to excit his classroom, the answer is 0

[@einherz]

infinity lol

[@pecareca6735]

Who will tell him its spelled exist, not excist

[@thunderpokemon2456]

I guess his accent

[@wMexso]

10 views in 4 mins? bro fell off