# How to solve 2^X = X^2

• April 23rd 2009, 01:59 PM
supersaiyan
How to solve 2^X = X^2
$f(x) = x^2$
$g(x) = 2^X$

Find regions where $f(x) > g(x)$
Is it possible to solve this algebraically or only guess and check?
by guess and check I mean subbing different values for x
• April 23rd 2009, 03:09 PM
mr fantastic
Quote:

Originally Posted by supersaiyan
$f(x) = x^2$
$g(x) = 2^X$

Find regions where $f(x) > g(x)$
Is it possible to solve this algebraically or only guess and check?
by guess and check I mean subbing different values for x

x = 2 and x = 4 are obvious solutions to f(x) = g(x).

To solve f(x) = g(x) algebraically would require using the Lambert W-function.