Answer
$$\text{undefined}$$
Work Step by Step
We simplify as follows:
$$\log_3 (\log_2 \frac{1}{8})=\log_3 (\log_22^{-3})=\log_3(-3\log_22)=\log_3(-3(1))=\log_3-3=\text{ undefined }$$(since the logarithm is not defined for negative real numbers).