a) Với $x=a^{3}b^{2}\sqrt{c}$

$\log_{a}x=\log_{a}a^{3}b^{2}\sqrt{c}$

= $\log_{a}a^{3}+\log_{a}b^{2}+\log_{a}\sqrt{c}$

= $3+2\log_{a}b+\frac{1}{2}\log_{a}c$

= $3+2.3+\frac{1}{2}(-2)=8$

b) Với $x=\frac{a^{4}\sqrt[3]{b}}{c^{3}}$, ta có:

$\log_{a}x=\log_{a}\frac{a^{4}\sqrt[3]{b}}{c^{3}}$

= $\log_{a}a^{4}+\log_{a}\sqrt[3]{b}-\log_{a}c^{3}$

= $4+\frac{1}{3}\log_{a}b-3\log_{a}c$

= $4+\frac{1}{3}.3-3(-2)=11$