How do you solve this?

xln(x)−6+2ln(x)−3x=0

Thank you!

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- Oct 23rd 2008, 07:56 AMgearshifterLn Question
How do you solve this?

xln(x)−6+2ln(x)−3x=0

Thank you! - Oct 23rd 2008, 01:42 PMmr fantastic
- Oct 23rd 2008, 02:41 PMPeritus
$\displaystyle

\begin{gathered}

x\ln x - 6 + 2\ln x - 3x = 0 \hfill \\

\Leftrightarrow (x + 2)\ln x = 3x + 6 \hfill \\

\Leftrightarrow \ln x = \frac{{3x + 6}}

{{x + 2}} = 3 \hfill \\

x = e^3 \hfill \\

\end{gathered} $