# Math Help - Solving this eqn?

1. ## Solving this eqn?

Hi,

I'm not quite sure how to tackle this equation:

-x=lnx

How do I solve for x? All I know is there is one real value of x, and that is ~.567. Is there a tidy expression for x, and if not, is there a name for this occurrence, or even this type of eqn?

Thanks,
B

2. Originally Posted by fwlksajzxlc
Hi,

I'm not quite sure how to tackle this equation:

-x=lnx

How do I solve for x? All I know is there is one real value of x, and that is ~.567. Is there a tidy expression for x, and if not, is there a name for this occurrence, or even this type of eqn?

Thanks,
B
$-x = \ln x \Rightarrow e^{-x} = x \Rightarrow 1 = x e^x$.

Therefore $x = W(1)$ where $W$ is the increasingly well known Lambert W-function (eg. see Lambert W-Function -- from Wolfram MathWorld. You can search MHF for various other questions where it's been used.)

3. Thank you mr fantastic.

B