Áp dụng công thức Lôgarit, ta có:

a) $4^{\log _{2}3}$

= $2^{2}^{\log _{2}3}$

= $2^{\log _{2}3^{2}}$

= $3^{2}=9$

Vậy $4^{\log _{2}3}=9$

b) $27^{\log _{9}2}$

= $3^{3\frac{1}{2}}^{\log _{3}2}$

= $2^{\frac{3}{2}}=2\sqrt{2}$

Vậy $27^{\log _{9}2}=2\sqrt{2}$

c) $9^{\log _{\sqrt{3}}2}$

= $\sqrt{3}^{4}^{\log _{\sqrt{3}}2}$

= $\sqrt{3}^{\log _{\sqrt{3}}2^{4}}$

= $2^{4}=16$

Vậy $9^{\log _{\sqrt{3}}2}=16$

d) $4^{\log _{8}27}$

= $2^{2}^{\log _{2}3}$

= $3^{2}=9$

Vậy  $4^{\log _{8}27}=9$