# solving e^x=5x+1

• Oct 28th 2012, 05:55 AM
narjsingh
solving e^x=5x+1
solving
e^x=5x+1
thanks
• Oct 28th 2012, 06:12 AM
Kyood
Re: solving e^x=5x+1
there is no exact solution for power-algebric equation
• Oct 28th 2012, 06:43 AM
skeeter
Re: solving e^x=5x+1
Quote:

Originally Posted by narjsingh
solving e^x=5x+1

one solution determined by "observation" is ...

$\displaystyle x = 0$

the other solution can be approximated using technology ...

$\displaystyle x \approx 2.6603991$
• Oct 28th 2012, 07:59 AM
JJacquelin
Re: solving e^x=5x+1
The non-evident root cannot be expressed analyticaly with the combination of a finite number of usual functions.
It can be erxpressed with infinite series (complicated, not useful in practice)
Usally, this kind of equation is solved thanks to numerical computation.
The root can be expressed on a closed form thanks to the Lambert W function :
x = -W(X) where X = -(exp(-1/5)-1)/5
• Oct 28th 2012, 09:36 AM
Kyood
Re: solving e^x=5x+1
Quote:

Originally Posted by skeeter
one solution determined by "observation" is ...

$\displaystyle x = 0$

the other solution can be approximated using technology ...

$\displaystyle x \approx 2.6603991$

In this case, It is ok, but in general it is diffecult to solve such equation directly
for example : solve : e^x=x+2
• Oct 28th 2012, 10:27 AM
JJacquelin
Re: solving e^x=5x+1
Quote:

Originally Posted by Kyood
In this case, It is ok, but in general it is diffecult to solve such equation directly
for example : solve : e^x=x+2

solve exp(x)=x+2 for x - Wolfram|Alpha
• Oct 28th 2012, 11:45 AM
skeeter
Re: solving e^x=5x+1
Quote:

Originally Posted by Kyood
In this case, It is ok, but in general it is diffecult to solve such equation directly
for example : solve : e^x=x+2

I'm pleased that my solution meets your approval ... in "this case".
• Oct 28th 2012, 12:41 PM
Kyood
Re: solving e^x=5x+1
Very nice, skeeter,
you used a special function W(x) which consedered as an approximate solutuion.
• Oct 28th 2012, 01:10 PM
skeeter
Re: solving e^x=5x+1
Quote:

Originally Posted by Kyood
Very nice, skeeter,
you used a special function W(x) which consedered as an approximate solutuion.

no ... I just solved $\displaystyle e^x - 5x - 1 = 0$ with a calculator.
• Oct 29th 2012, 06:28 AM
divyaprashanth07
Re: solving e^x=5x+1
$\displaystyle \int_{0}^{\pi}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx =\frac{22}{7}-\pi$
• Oct 29th 2012, 03:40 PM
skeeter
Re: solving e^x=5x+1
Quote:

Originally Posted by divyaprashanth07
$\displaystyle \int_{0}^{\pi}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx =\frac{22}{7}-\pi$

... what does this incorrectly evaluated definite integral have to do with this thread?