Solving Equation (Exponential)

**Simplicity** · March 23rd 2011, 07:00 AM

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.

**Prove It** · March 23rd 2011, 07:11 AM

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.

**TheChaz** · March 23rd 2011, 07:12 AM

From the first line, multiply both sides by -3.
Then you'll be in a form where you can use...
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