How do you solve this? xln(x)−6+2ln(x)−3x=0 Thank you!

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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.

$\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} $

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