比大小 \( 3^\pi和\pi^3 \)

\( \because  \log3^\pi=\pi \times \log3 \approx 3.14 \times 0.4771 =1.498294 \)

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

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

\( 又  \frac{22}{7} \approx 3.142857 > \pi \)

\(  \therefore 3^\pi  >   \frac{22}{7}^3  > \pi^3 \)