When solving

$\ln(x^2+1) = \ln(x) + 2$

I'm getting stuck at

$e^2 = \dfrac{x^2+1}{x}$

How do I isolate $x$?

  • 1
    $\begingroup$ Write as a quadratic equation and solve for $x$. $\endgroup$ May 27 '12 at 12:18

$$e^2=\frac{x^2+1}{x}\Longleftrightarrow x^2-e^2x+1=0$$

and you have a simple quadratic to solve.

  • 2
    $\begingroup$ I think the OP doesn't know how to. Assuming he doesn't, I'd add the quadratic solution : $ax^2+bx+c$, the solutions are $ x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$. $\endgroup$
    – Inquest
    May 27 '12 at 12:34
  • $\begingroup$ Don't worry, I do know about how to solve quadratic equations. ;-) $\endgroup$ May 27 '12 at 16:57

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