比大小 $3^\pi和\pi^3$

$\because  \log3^\pi=\pi \times \log3 \approx 3.14 \times 0.4771 =1.498294$

$\log  \frac{22}{7}^3=3 \times (\log2+\log11-\log7)$

$\approx 3 \times (0.3010+1.0414-0.8451) =1.4919$

$又  \frac{22}{7} \approx 3.142857 > \pi$

$\therefore 3^\pi  >   \frac{22}{7}^3  > \pi^3$