Can You Solve this Exponential Equation Involving Pi? Think out-side-the-Box| Step-by-Step Tutorial

[tharanathakula]

I simplified mentally and got the value of X= 0.421 to be exact and it took just 5 minutes.

[susennath]

After a long time a master piece equation

[waheisel]

With pi and e in the same equation I was looking for a connection to Euler's identity! Thanks as always PreMath!

[zplusacademy]

Very nice sir as always .... expressing maverick

[devondevon]

pi^1-x = e^x
(1-x)ln pi = x take the natural log of both sides (ln e^x =x)
1.1447- 1.1447x = x
1.1447 = 2.1447x
1.1447/2.1447=x
0.53374 Answer

[yassine]

It's much easier to multiply both sides by pi^x

[ycart_tech]

e^x=π^(1-x), therefore, ln(π^(1-x))=x and finally 1/1-x=ln(π) or x~0.533)

[montynorth]

Thanks for a nice problem and your simple solution.
I wasn't up to speed that the natural log of e^x equals x, so I used x.log e
(1-x)log pi = x.log e
(1-x)log 3.14 = x.log 2.718282
(1-x) 0.4969 = x (0.4343)
0.4969 - 0.4969x = 0.4343x
0.4969 = 0.9312x
x = 0.4969/0.9312 = 0.534

[learnenglishwithsanafarhan]

Wow great 💯
Absolutely an amazing content👏
Cleard my concept.🤗
Share more vedio💥💯🌹✨

[sohommajumder]

Can you suggest any book to get these kinds of problems? Please?

[LexxUrsus]

very good! can i ask a task? You need compare π^e and e^π without calculator. It will be funny task.

[jbreezy]

I was thinking e^iπ = 1 or something like that but I just realized that there's no i here

[sameerqureshi-khcc]

A simple and to-the-point approach! 😊👍🌹

[hassanalihusseini]

Interesting that e does not play a role in the final result.

[geoffreyparfitt]

I think it would be better practice to get x in one place before taking logs. Less steps and to me more elegant.

[j.r.]

I often come here to comment that I used a different method from the one in the video to solve the problem. But today I have to say that I used exactly the official method -- every single step, in order! A strange feeling. :)

[tharanathakula]

I regret that I have made a mistake in my solution below that was I added the PI^x and e^xinstead of multiplying the exact value of x is 0.534