How do you find an analytical solution for 3^x-x=4?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
|
0
|
||||||||||||
|
closed as off topic by J.C. Ottem, Denis Serre, quid, Daniel Litt, Will Jagy Sep 13 2011 at 21:21 |
|
6
|
If you want, you can use Lambert's W function. Let $z:=x+4$, so that the equation becomes $3^{z-4}=z$, so that $-3^{-4}=-z3^{-z}$, which upon inverting with Lambert's $W$ gives: $x=-\frac{W(-\ln(3)3^{-4})}{\ln(3)}-4$ In particular, $W(r)$ has a nice taylor expansion: $W(r)=\sum_{n=1}^\infty \frac{(-1)^{n-1}n^{n-2}}{(n-1)!}r^n$ |
||
|
|
