Solving $e^x = 6x$ for $x$ without a graph. Throughout my high school career I was always told that an equation of this sort ( $e^x = 6x$ for example) couldn't be solved algebraically. However I feel that there may be a way (and you may be out there saying "of course there is a way") I know that it can be solved graphically, but is there any other way(s) to solve this equation: $$e^x = 6x$$
**Without graphing or using a equation solver **

I am a fan of fixed point iteration because I find it easy to set up.  You want to work your equation into the form $x=f(x)$ where the derivative of $f(x)$ at the root is small and certainly less than $1$ in absolute value.  Then pick a reasonable starting value for $x_0$ and iterate $x_{i+1}=f(x_i)$.  As logs are slowly varying I would write this as 
$$x=\log (6x)=\log (6) + \log (x)$$
A starting value of $x_0=\log(6)$ looks reasonable.  After a couple dozen iterations in a spreadsheet (love copy-down) it has converged to about $2.833148$
