# Logarithms - Find the solution of $\ln(x^2+1) = \ln(x) + 2$, how to isolate $x$ in a meaningful way?

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 $x$?

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Write as a quadratic equation and solve for $x$. – Ayman Hourieh May 27 '12 at 12:18

## 1 Answer

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

and you have a simple quadratic to solve.

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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 $x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$. – Inquest May 27 '12 at 12:34
Don't worry, I do know about how to solve quadratic equations. ;-) – Miroslav Cetojevic May 27 '12 at 16:57