Answer
a) $\log_4 8=\dfrac{3}{2}$
b) $8^{2/3}=4$
Work Step by Step
a) Since $\log_by=x$ is equivalent to $y=b^x$, the given equation, $
4^{3/2}=8
,$ above, in logarithmic form, is equivalent to
\begin{array}{l}\require{cancel}
\log_4 8=\dfrac{3}{2}
.\end{array}
b) Since $\log_by=x$ is equivalent to $y=b^x$, the given equation, $
\log_8 4=\dfrac{2}{3}
,$ above, in exponential form, is equivalent to
\begin{array}{l}\require{cancel}
8^{2/3}=4
.\end{array}