Answer
20
Work Step by Step
When the system is in equilibrium, we can write
Buoyant force = weight of logs + weight of people
$F_{B}=m_{l}g+m_{p}g$
According to the Principle of Archimedes', we can rewrite the above equation as follows.
$V_{w}\rho_{w}g=V_{l}\rho_{l}g+m_{p}g$
When the logs become minimum, $V_{w}=V_{l}$ So,
$V_{l}\rho_{w}g=V_{l}\rho_{l}g+m_{p}g$
$V_{l}=\frac{m_{p}}{\rho_{w}-\rho_{l}}$ ; Let's plug known values into this equation.
$V_{l}=\frac{4\times80\space kg}{1000\space kg/m^{3}-725\space kg/m^{3}}=1.16\space m^{3}$
Volume of one log = $\pi(0.08\space m)^{2}(3\space m)=0.06\space m^{3}$
Number of logs needed = $\frac{V_{l}}{0.06\space m^{3}}=\frac{1.16\space m^{3}}{0.06\space m^{3}}=19.3$
Thus, at least 20 logs are needed.
