Answer
$ln(3\pm2\sqrt 2)\approx\pm1.763$
Work Step by Step
Step 1. Let $u=e^{x}$ and rearrange to get $u^2+1=6u \longrightarrow u^2-6u+1=0 \longrightarrow u=\frac{6\pm\sqrt {36-4}}{2}=3\pm2\sqrt 2$
Step 2. For $e^x=3+2\sqrt 2$, we have $x=ln(3+2\sqrt 2)\approx1.763$
Step 3. For $e^x=3-2\sqrt 2$, we have $x=ln(3-2\sqrt 2)\approx-1.763$
Step 4. Check, $x=ln(3\pm2\sqrt 2)\approx\pm1.763$ fit the original equation.
