# Solving Equation (Exponential)

• Mar 23rd 2011, 07:00 AM
Simplicity
Solving Equation (Exponential)
I need to solve:
$\frac{1}{x} e^{-\frac{3}{x}} = 0.1086$

My method:
$\frac{1}{x} e^{-\frac{3}{x}} = 0.1086$
$e^{-\frac{3}{x}} = 0.1086x$
$\ln \left(e^{-\frac{3}{x}} \right)= \ln (0.1086x)$
$-\frac{3}{x} = \ln (0.1086) + \ln (x)$

But I'm stuck from here. Don't understand what to do. (Worried)
• Mar 23rd 2011, 07:11 AM
Prove It
I seriously doubt that you will be able to find an exact value for $\displaystyle x$. Just use a numerical method and/or some technology.
• Mar 23rd 2011, 07:12 AM
TheChaz
From the first line, multiply both sides by -3.
Then you'll be in a form where you can use...
Lambert W function - Wikipedia, the free encyclopedia