#### Answer

$\dfrac {1}{2}\log _{2}5+\dfrac {3}{2}\log _{2}r-\dfrac {5}{2}\log _{2}z$

#### Work Step by Step

$\log _{2}\sqrt {\dfrac {5r^{3}}{z^{5}}}=\log _{2}5^{1/2}\times r^{3/2}\times z^{-5/2}=\dfrac {1}{2}\log _{2}5+\dfrac {3}{2}\log _{2}r-\dfrac {5}{2}\log _{2}z$