Solving Algebraic Equations: How to Solve 0 = 7.5x - 50ln(2x + 1) - 600

[danago]

Hey. How can i solve this algebraically?

$$0 = 7.5x - 50\ln (2x + 1) - 600$$

Ive graphed it and done it like that, but id like to be able to obtain an exact answer. Anyone able to help me?

Thanks,
Dan.

EDIT: Oops, misspelled the title :P

 

[courtrigrad]

I don't think it can be solved using elementary functions, because you get the equation in the form $e^{x} = x$. You have to use the Lambert W-function.

http://mathworld.wolfram.com/LambertW-Function.html

 

[danago]

oh ok. Well thanks for confirming that :)