Find the solution of this ln equation

[transgalactic]

find the solution of this ln equation:
ax=lnx

i tried:
$$e^{(ax)}=x$$
$$e^{(ax)}-x=0$$

what to do next??
i thought of building a taylor series around 0 for ln
but ln(0) is undefined

??

 

[Toftarn]

I'm not entirely sure, but I think such equations must be solved with a numerical method, such as Newton-Rhapson.

 

[epenguin]

When there is any solution there are two I think.