Q = {log _a}left( {asqrt b } ight) - {log _{sqrt a }}left( {asqrt[4]{b}} ight) + {log _{sqrt[3]{b}}}b

$\begin{array}{l} Q = {\log _a}\left( {a\sqrt b } \right) - 2{\log _a}\left( {a\sqrt[4]{b}} \right) + 3{\log _b}b\\ = {\log _a}\left( {a\sqrt b } \right) - {\log _a}\left( {{a^2}\sqrt b } \right) + 3\\ = {\log _a}\frac{{a\sqrt b }}{{{a^2}\sqrt b }} + 3\\ = {\log _a}\frac{1}{a} + 3 = - 1 + 3 = 2 \end{array}$