For three positive integers p, q, r, x^p q^2=y^q r=z^p^2 r and r = pq +1 such that 3,3 log_y x, 3 log_z y, 7 log_x z are in A.P. with common…

For three positive integers $\displaystyle \mathrm{p}, \mathrm{q}, \mathrm{r}, x^{p q^2}=y^{q r}=z^{p^2 r}$ and $\displaystyle \mathrm{r}=\mathrm{pq}+1$ such that $\displaystyle 3,3 \log _y x, 3 \log _{\mathrm{z}} \mathrm{y}$, $\displaystyle 7 \log _x z$ are in A.P. with common difference $\displaystyle \frac{1}{2}$. Then $\displaystyle \mathrm{r}-\mathrm{p}-\mathrm{q}$ is equal to