Polytropic index x is given by

A

$$\frac{\log \left( \frac {p_2}{p_1}\right)}{\log \left( \frac {v_1}{v_2}\right)}$$

B

$$\frac{\log \left( \frac {p_1}{p_2}\right)}{\log \left( \frac {v_1}{v_2}\right)}$$

C

$$\frac{\log \left( \frac {v_1}{v_2}\right)}{\log \left( \frac {p_2}{p_1}\right)}$$

D

$$\frac{\log \left( \frac {v_2}{v_1}\right)}{\log \left( \frac {p_2}{p_1}\right)}$$