Logarithm value of product

Let $p^3 = q^4 = r^5 = s^6 = k$. Then: $p = k^{1/3}, \quad q = k^{1/4}, \quad r = k^{1/5}, \quad s = k^{1/6}$

Now, $pqr = k^{1/3 + 1/4 + 1/5} = k^{\frac{20 + 15 + 12}{60}} = k^{47/60}$. Since $s = k^{1/6}$, we have $k = s^6$.

Thus, $pqr = (s^6)^{47/60} = s^{47/10}$.

Therefore, $\log_s (pqr) = \frac{47}{10}$.