Áp dụng công thức Lôgarit, ta có:

a)  $\log _{2}\frac{1}{8}$

= $\log _{2}2^{-3}=-3$

Vậy $\log _{2}\frac{1}8=-3$

b) $\log _{\frac{1}{4}}2$

= $\log _{2^{-2}}2$

= $\frac{-1}{2}\log _{2}2=\frac{-1}{2}$

Vậy $\log _{\frac{1}{4}}2=\frac{-1}{2}$

c) $\log _{3}\sqrt[4]{3}$

= $\log _{3}3^{\frac{1}{4}}$

= $\frac{1}{4}\log _{3}3=\frac{1}{4}$

Vậy $\log _{3}\sqrt[4]{3}=\frac{1}{4}$

d) $\log _{0,5}0,125$

= $\log _{0,5}(0,5^{3})$

= $3\log _{0,5}0,5=3$

Vậy $\log _{0,5}0,125=3$