# Math Help - Ln Question

1. ## Ln Question

How do you solve this?

xln(x)−6+2ln(x)−3x=0

Thank you!

2. Originally Posted by gearshifter
How do you solve this?

xln(x)−6+2ln(x)−3x=0

Thank you!
Are you sure about the red x ....... If the equation is correctly stated, you should use a numerical method (ie. technology) to get an approximate solution.

3. $
\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}$