# Question #9b0dd

x= $\ln \left\{\frac{3 \pm \sqrt{5}}{2}\right\}$
Consider ${e}^{x}$ as t and the given equation is transformed into a quadratic equation ${t}^{2}$ -3t+1=0. Use quadratic formula to solve for t= $\frac{3 \pm \sqrt{5}}{2}$. Now substitute ${e}^{x}$ for t
${e}^{x}$ =$\frac{3 \pm \sqrt{5}}{2}$
and take log on both sides, to get x= $\ln \left\{\frac{3 \pm \sqrt{5}}{2}\right\}$