Answer
{$\frac{1}{2}(\frac{\log 6}{\log 3}-1)$}, {$0.3155$}
Work Step by Step
Step 1: $3^{2x+1}=6$
Step 2: $\log 3^{2x+1}=\log 6$
Step 3: $(2x+1)\log 3=\log 6$
Step 4: $(2x+1)=\frac{\log 6}{\log 3}$
Step 5: $2x=\frac{\log 6}{\log 3}-1$
Step 6: $x=\frac{1}{2}(\frac{\log 6}{\log 3}-1)\approx0.3155$
Therefore, the exact solution is {$\frac{1}{2}(\frac{\log 6}{\log 3}-1)$} whereas the four decimal approximation is {$0.3155$}.
