Answer
$log_3(\frac{3-\sqrt {5}}{2})\approx- 0.876$
$log_3(\frac{3+\sqrt {5}}{2})\approx0.876$
Work Step by Step
Step 1. Let $u=3^x$, we have $u^2-3u+1=0 \longrightarrow u=\frac{3\pm\sqrt {9-4}}{2}=\frac{3\pm\sqrt {5}}{2}$
Step 2. For $3^x=\frac{3-\sqrt {5}}{2}$, we have $x=log_3(\frac{3-\sqrt {5}}{2})\approx- 0.876$
Step 3. For $3^x=\frac{3+\sqrt {5}}{2}$, we have $x=log_3(\frac{3+\sqrt {5}}{2})\approx0.876$
