#### Answer

$\log _{b}x^{\frac {17}{6}}y^{\frac {29}{12}}$

#### Work Step by Step

$\dfrac {1}{3}\log _{b}x^{4}y^{5}-\dfrac {3}{4}\log _{b}x^{2}y=\log _{b}\left( x^{4}y^{5}\right) ^{\frac {1}{3}}+\log _{b}\left( x^{2}y\right) ^{\frac {3}{4}}=\log _{b}\left( \left( x^{4}y^{5}\right) ^{\frac {1}{3}}\times \left( x^{2}y\right) ^{\frac {3}{4}}\right) =\log _{b}x^{\frac {17}{6}}y^{\frac {29}{12}}$