It doesn't really matter when you do it. Personally I found it easiest to take the log after simplifying to (e/π)^x=π^e/e^π since there is then a single instance of x on the left side and the right side is a constant.
What a long ride! This equation could be solved in 5 lines if you take log on both sides right from the begining including special care for the existence of the log. Even it is not bad to play with expontial properties I am still asking why doing complicated when it is simple ???
e^x + pi = pi^x + e x + pi = ln(pi)x + e × ln(pi) x - ln(pi)x = e × ln(pi) - pi (1 - ln(pi))x = e × ln(pi) - pi x = e × ln(pi) - pi / 1 - ln(pi) x ≈ 0.206552
Very complicated:
e^(x+pi)=pi^(x+e) => ln(e^(x+pi))=ln(pi^(x+e))
=> (x+pi)=(x+e)ln(pi) => x(1-ln(pi))=e•ln(pi)-pi
=> x=(e•ln(pi)-pi)/(1-ln(pi))
That's all.
Alright Boss...
Thanks for sharing your brilliant approach.👍
@Андрей , are you from Russia?
same to me
@@hossian1776 I was born in Russia
@ Where do you live now?
I agree with comment A. Take the ln both sides first.
Alright Boss 😊
It doesn't really matter when you do it. Personally I found it easiest to take the log after simplifying to (e/π)^x=π^e/e^π since there is then a single instance of x on the left side and the right side is a constant.
What a long ride! This equation could be solved in 5 lines if you take log on both sides right from the begining including special care for the existence of the log. Even it is not bad to play with expontial properties I am still asking why doing complicated when it is simple ???
Foarte frumoasă și interesantă ecuația, respectiv forma ei de prezentare și algoritmul de rezolvare. Felicitări! Sănătate și succes în continuare.
Bundle of thanks for praising and sharing your precious feedback 😌😊👍
Muy interesante video muchas gracias por compartir tan buena y didáctica explicación. 😊❤😊.
Many many Thanks 👍🤗😍
Thanks for sharing your precious feedback.
It means a lot for us.😍
@@MathBeast.channel-l9i las gracias siempre a ustedes, estos valiosos videos le servirán a mi hija a continuar sus estudios universitarios.
e^{x+x ➖ }+{pi+pi ➖ }=e^{x^2+pi^4}=e^pi^4x^2 e^pi^2^2x^2 e^pi^2^1x^1 e^pi^2^1^x (e x ➖ 2pie x+1). pi^{x+x ➖ }+{e+e ➖ }=pi^{x^2+e^2}=pi^e^2x^2 (pix ➖ 2epix+2).
You only have to use ln:
X+pi= (x+e)* ln( pi)
X( 1- ln(pi))= e* ln(pi) -pi
Division by. (1- ln(pi)) finished
Graph
y = e^x + pi
y = pi^x + e
Solution: x = e × ln(pi) - pi / 1 - ln(pi)
Intersection with the x-axis: Does not exist
Domain: -infinty
e^x + pi = pi^x + e
x + pi = ln(pi)x + e × ln(pi)
x - ln(pi)x = e × ln(pi) - pi
(1 - ln(pi))x = e × ln(pi) - pi
x = e × ln(pi) - pi / 1 - ln(pi)
x ≈ 0.206552
ePix-EPix=1]=X-X=X/X=X-1=1 X=1:
It seems that you only do this because you are obsessed with the act of writing.
x + π = (x + e)lnπ
x = (elnπ - π)/(1 - lnπ)
In C the answers are :
z = (e.ln(pi) - pi)/1 - ln(pi)
+ i.2k.pi/ 1- ln(pi), k € Z.
For k = 0 we find the real answer.