Math Challenge with factoring logarithm, needs urgent generous help!

Hi.
Doing Programming, I am quited stucked in some math problem.

Here is the problem.

ln(x)+ax=c

I need to factorizing in terms of x, so that I can derive the value for x.

such as x=00

Here, a and c are constant.

How can I make this?

There is no trivial way to solve this. Perhaps you could approximate it with Taylor Expansion.